A Complete Self Study Guide B. Arch (Bachelor of Architecture) Entrance Examination Mathematics>Chapter 18 - Trigonometry>EXERCISE>Q 10

HARD

JEE Main Paper 2A- B.Arch

IMPORTANT

Earn 100

The sum of the infinite series $\cot^{- 1} 2 + \cot^{- 1} 8 + \cot^{- 1} 18$ $+ \cot^{- 1} 32 + \dots$ is equal to

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Important Questions on Trigonometry

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JEE Main Paper 2A- B.Arch

IMPORTANT

A Complete Self Study Guide B. Arch (Bachelor of Architecture) Entrance Examination Mathematics>Chapter 18 - Trigonometry>EXERCISE>Q 11

If the equation

\tan θ + \sec θ = \sqrt{3}

, then the value of

θ \in (0, 2 π)

is

HARD

JEE Main Paper 2A- B.Arch

IMPORTANT

A Complete Self Study Guide B. Arch (Bachelor of Architecture) Entrance Examination Mathematics>Chapter 18 - Trigonometry>EXERCISE>Q 12

If

a_{1}, a_{2} \dots \dots, a_{n}

are in

AP

, with common difference,

d

, then, the sum of the following series is

\sin d (cosec a_{1} \cdot cosec a_{2} + cosec a_{2} \cdot cosec a_{3} + \dots \dots + cosec a_{n - 1} cosec a_{n})

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JEE Main Paper 2A- B.Arch

IMPORTANT

A Complete Self Study Guide B. Arch (Bachelor of Architecture) Entrance Examination Mathematics>Chapter 18 - Trigonometry>EXERCISE>Q 13

Statement

I :

The minimum value of

27^{\cos 2 x} 81^{\sin 2 x}

is

\frac{1}{243}

.
Statement

II :

The minimum value of

a \cos θ + b \sin θ

is

- \sqrt{a^{2} + b^{2}}

.

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JEE Main Paper 2A- B.Arch

IMPORTANT

A Complete Self Study Guide B. Arch (Bachelor of Architecture) Entrance Examination Mathematics>Chapter 18 - Trigonometry>EXERCISE>Q 14

\cos^{- 1} [\cos \{2 \cot^{- 1} (\sqrt{2} - 1)\}]

is equal to

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JEE Main Paper 2A- B.Arch

IMPORTANT

A Complete Self Study Guide B. Arch (Bachelor of Architecture) Entrance Examination Mathematics>Chapter 18 - Trigonometry>EXERCISE>Q 15

Let

(1 + \sqrt{1 + x}) \tan y = 1 + \sqrt{1 - x}

. Then,

\sin 4 y

is equal to

EASY

JEE Main Paper 2A- B.Arch

IMPORTANT

A Complete Self Study Guide B. Arch (Bachelor of Architecture) Entrance Examination Mathematics>Chapter 18 - Trigonometry>EXERCISE>Q 16

\sin \frac{π}{n} + \sin \frac{3 π}{n} + \sin \frac{5 π}{n} + \dots

to

n

terms is equal to

HARD

JEE Main Paper 2A- B.Arch

IMPORTANT

A Complete Self Study Guide B. Arch (Bachelor of Architecture) Entrance Examination Mathematics>Chapter 18 - Trigonometry>EXERCISE>Q 17

If

0 \leq x \leq \frac{π}{2}

and

81^{\sin^{2} x} + 81^{\cos^{2} x} = 30,

then

x

is equal to

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JEE Main Paper 2A- B.Arch

IMPORTANT

A Complete Self Study Guide B. Arch (Bachelor of Architecture) Entrance Examination Mathematics>Chapter 18 - Trigonometry>EXERCISE>Q 18

In a

∆ A B C,

tan

A . \tan B . \tan C = 9 .

For such triangles, if

\tan^{2} A + \tan^{2} B + \tan^{2} C = k,

then