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In any triangle $A B C$ , which is not right angled $Σ cos A . cosec B . cosec C$ is equal to

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Important Questions on Trigonometric Ratios and Identities

HARD

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Conditional Identities

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

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Conditional Identities

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 Ratios and Identities>Conditional Identities

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 Ratios and Identities>Conditional Identities

Let

P = \{θ : \sin θ - \cos θ = \sqrt{2} \cos θ\}

and

Q = \{θ : \sin θ + \cos θ = \sqrt{2} \sin θ\},

be two sets. Then

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Conditional Identities

Δ A B C

, if

\tan A + \tan B + \tan C = 6

and

\tan A \tan B = 2

then

\tan C =

……

HARD

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Conditional Identities

A > 0, B > 0

and

A + B = \frac{π}{6}

, then the minimum positive value of

(\tan A + \tan B)

is :

HARD

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Conditional Identities

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

and

x \sin θ = y \cos θ

, then

x^{2} + y^{2}

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Mathematics>Trigonometry>Trigonometric Ratios and Identities>Conditional Identities

The value of

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

MEDIUM

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Conditional Identities

In a triangle

A B C, {(\tan \frac{A}{2} \tan \frac{B}{2} \tan \frac{C}{2})}^{2} \leq

HARD

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Conditional Identities

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

HARD

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Conditional Identities

Let

α

and

β

be non zero real numbers such that

2 (\cos β - \cos α) + \cos α \cos β = 1

. Then which of the following is/are true?

MEDIUM

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Conditional Identities

A, B, C

are the angle of

Δ A B C

then

\cot A \cot B + \cot B \cot C + \cot A \cot C =

HARD

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Conditional Identities

The value of

\sec^{- 1} (\frac{1}{4} \sum_{k = 0}^{10} \sec (\frac{7 π}{12} + \frac{k π}{2}) \sec (\frac{7 π}{12} + \frac{(k + 1) π}{2}))

in the interval

[- \frac{π}{4}, \frac{3 π}{4}]

equals

MEDIUM

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Conditional Identities

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

then

|\cot (\frac{π}{4} + \frac{θ}{2})|

is equals to:

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Conditional Identities

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:

MEDIUM

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Conditional Identities

The value of

\cos^{3} (\frac{π}{8}) . \cos (\frac{3 π}{8}) + \sin^{3} (\frac{π}{8}) . \sin (\frac{3 π}{8})

is:

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Conditional Identities

The value of

\sin 18 °

is …..

MEDIUM

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Conditional Identities

The expression

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

can be written as :

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Conditional Identities

Δ A B C;

with usual notations,

\frac{b s i n B - c s i n C}{\sin (B - C)}

= ……

MEDIUM

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Conditional Identities

The sides of a triangle inscribed in a given circle subtend angles

α, β, γ

at the center. The minimum value of the

A . M .

\cos (α + \frac{π}{2}), \cos (β + \frac{π}{2})

and

\cos (γ + \frac{π}{2})

is equal to

In any triangle ABC, which is not right angled Σ cos A . cosec B . cosec C is equal to

Important Questions on Trigonometric Ratios and Identities

Learn and Prepare for any exam you want !

In any triangle $A B C$ , which is not right angled $Σ cos A . cosec B . cosec C$ is equal to