For any θ ∈ π 4 , π 2 , the expression 3 sin θ - cos θ 4 + 6 sin θ + cos θ 2 + 4 s i n 6 θ equals:

13 - 4 cos 2 θ + 6 sin 2 θ cos 2 θ

13 - 4 cos 4 θ + 2 sin 2 θ cos 2 θ

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Sum of squares of all trigonometric ratios has minimum value as $λ$ , then the value of $\frac{500}{λ}$ is :

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Important Questions on Trigonometric Functions

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Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Functions of Sum and Difference of Two Angles

The integer part of the number

\sum_{k = 0}^{44} \frac{1}{cosk ° \cos (k + 1) °}

(\sin 1 ° = 0.0174524)

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Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Functions of Sum and Difference of Two Angles

A B C D

is a trapezium such that

A B

and

C D

are parallel and

B C ⊥ C D

. If

∠ A D B = θ

B C = p

and

C D = q

, then

A B

is equal to

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Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Functions of Sum and Difference of Two Angles

\cos α + \cos β = \frac{3}{2} and \sin α + \sin β = \frac{1}{2}

and

θ

is the arithmetic mean of

α & β,

then

\sin 2 θ + \cos 2 θ

is equal to:

EASY

Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Functions of Sum and Difference of Two Angles

\frac{\sin A - \sin B}{\cos A + \cos B}

is equal to

EASY

Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Functions of Sum and Difference of Two Angles

∆ A B C

, with usual notations, if

a, b, c

are in

A . P .

, then

a \cos^{2} (\frac{C}{2}) + c \cos^{2} (\frac{A}{2}) =

EASY

Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Functions of Sum and Difference of Two Angles

If an angle

A

of a

Δ A B C

satisfies

5 \cos A + 3 = 0

, then the roots of the quadratic equation

9 x^{2} + 27 x + 20 = 0

are

EASY

Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Functions of Sum and Difference of Two Angles

In a

Δ A B C

\frac{a}{b} = 2 + \sqrt{3}

, and

∠ C = 60 ° .

Then the ordered pair

(∠ A, ∠ B)

is equal to:

MEDIUM

Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Functions of Sum and Difference of Two Angles

The number of real numbers

λ

for which the equality

\frac{\sin (λ α)}{\sin α} - \frac{\cos (λ α)}{\cos α} = λ - 1,

holds for all real

α

which are not integral multiples of

\frac{π}{2}

is-

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Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Functions of Sum and Difference of Two Angles

The value of

\sum_{k = 1}^{13} \frac{1}{\sin (\frac{π}{4} + \frac{(k - 1) π}{6}) \sin (\frac{π}{4} + \frac{k π}{6})}

is equal to

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Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Functions of Sum and Difference of Two Angles

s i n^{4} α + 4 c o s^{4} β + 2 = 4 \sqrt{2} s i n α c o s β

α, β \in [0, π]

, then

c o s (α + β) - c o s (α - β)

is equal to

MEDIUM

Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Functions of Sum and Difference of Two Angles

\frac{\sqrt{3}}{\sin (20^{o})} - \frac{1}{\cos (20^{o})} =

EASY

Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Functions of Sum and Difference of Two Angles

12 \cot^{2} θ - 31 cosec θ + 32 = 0,

then the value of

s i n θ

EASY

Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Functions of Sum and Difference of Two Angles

\sin 15^{o} =

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Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Functions of Sum and Difference of Two Angles

x \sin^{3} θ + y \cos^{3} θ = \sin θ \cos θ

and

x \sin θ = y \cos θ

, then

x^{2} + y^{2}

EASY

Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Functions of Sum and Difference of Two Angles

\sin θ - \cos θ = 1

,

then the value of

\sin^{3} θ - \cos^{3} θ

is equal to

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Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Functions of Sum and Difference of Two Angles

Let

f_{k} (x) = \frac{1}{k} (\sin^{k} x + \cos^{k} x)

where

x \in R

and

k \geq1

. Then

f_{4} (x) - f_{6} (x)

equals

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Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Functions of Sum and Difference of Two Angles

cosec θ = \frac{p + q}{p - q} (p \neq q, p \neq 0),

then

|\cot (\frac{π}{4} + \frac{θ}{2})|

is equals to:

MEDIUM

Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Functions of Sum and Difference of Two Angles

The expression

\frac{tanA}{1 - cotA} + \frac{cotA}{1 - tanA}

can be written as :

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Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Functions of Sum and Difference of Two Angles

For any

θ \in (\frac{π}{4}, \frac{π}{2}),

the expression

3 {(\sin θ - \cos θ)}^{4} + 6 {(\sin θ + \cos θ)}^{2} + 4 {s i n}^{6} θ

equals:

MEDIUM

Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Functions of Sum and Difference of Two Angles

2 sin (θ + \frac{π}{3}) = cos (θ - \frac{π}{6})

, then

tan θ =

Sum of squares of all trigonometric ratios has minimum value as λ, then the value of 500λ is :

Important Questions on Trigonometric Functions

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Sum of squares of all trigonometric ratios has minimum value as $λ$ , then the value of $\frac{500}{λ}$ is :