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

The equation y = sin x · sin x + 2 - sin 2 ( x + 1 ) represents a straight line lying in:

third and fourth quadrants only

first, third and fourth quadrants

second and third quadrants only

first, second and fourth quadrants

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If $\tan θ = n \tan ϕ,$ then the maximum value of $\tan^{2} (θ - ϕ)$ 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 maximum value of

\sin (x + \frac{π}{6}) + \cos (x + \frac{π}{6})

in the interval

(0, \frac{π}{2})

is attained at

HARD

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:

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

The value of

\sin^{2} 38 ° + \sin^{2} 52 ° + \sin^{2} 30 ° - \tan^{2} 45 °

is equal to:

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

The numerical value of $\sin 12 ° \cdot \sin 48 ° \cdot \sin 54 °$ is equal to

EASY

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

c o s (α + β) = \frac{3}{5}, \sin (α - β) = \frac{5}{13}

and

0 < α, β < \frac{π}{4},

then

\tan (2 α)

is equal to:

HARD

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

0 ° < A, B < 45 °, \cos (A + B) = \frac{24}{25}

and

\sin (A - B) = \frac{15}{17}

, then

\tan 2 A

is:

EASY

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

What is the value of $\cos^{2} 5 ° + \cos^{2} 10 ° +_____+ \cos^{2} 90 °$

HARD

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

The value of

\cos^{2} 10 ° - \cos 10 ° \cos 50 ° + c o s^{2} 50 °

EASY

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

The equation

y = \sin x \cdot \sin (x + 2) - \sin^{2} (x + 1)

represents a straight line lying in:

EASY

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

Find the value of

cosec (60^{o} + A) - \sec (30^{o} - A) + \frac{cosec 49^{o}}{\sec 41^{o}}

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:

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}) =

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

The value of

\frac{3 (1 - 2 \sin^{2} x)}{\cos^{2} x - \sin^{2} x}

is:

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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 =

HARD

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

HARD

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

cosec θ + \cot θ = \frac{1}{3},

then

θ

lies in the

EASY

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

The value of

s i n 10 ° s i n 30 ° s i n 50 ° s i n 70 °

is:

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 :

If tan⁡θ=ntan⁡ϕ, then the maximum value of tan2⁡(θ-ϕ) is

Important Questions on Trigonometric Functions

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If $\tan θ = n \tan ϕ,$ then the maximum value of $\tan^{2} (θ - ϕ)$ is