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Introduction to Trigonometry

Multiple Choice Questions

361. Given that 16 cot A = 12, then the value of

fraction numerator sinA plus cosA over denominator sinA minus cosA end fraction

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362. The value of x if tan 3x = (sin 45° . cos 45°) sin 30°:
14°
15°
16°
16°

15°

tan 3 straight x space equals space open parentheses fraction numerator 1 over denominator square root of 2 end fraction cross times fraction numerator 1 over denominator square root of 2 end fraction close parentheses divided by 1 half equals 1 half cross times 2 over 1 equals 1 equals tan 45 degree comma space space 3 straight x space equals space 45 degree space space rightwards double arrow space straight x space equals space 15 degree

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363. The value of x if cos x = cos 60°. cos 30° + sin 60°. sin 30°:

20°
30°
60°
60°

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364. The value of (1 + cot² θ) (1 – cos θ) (1 + cos θ ) is

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365.

The value of $fraction numerator cosA over denominator 1 minus tanA end fraction plus fraction numerator sinA over denominator 1 minus cotA end fraction$ is

cos A + sin A
sin A – cos A
tan A + cot A
tan A + cot A

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366. tan 10°. tan 75°. tan 15°. tan 80° is

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367. tan 1°. tan 2°. tan 3°................tan 89° is

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368.

open parentheses fraction numerator tan space 20 degree over denominator cosec space 70 degree end fraction close parentheses squared plus open parentheses fraction numerator cot space 20 degree over denominator sec space 70 degree end fraction close parentheses squared

6
$1 half$
0
0

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369. If A, B, C are the interior angles of a triangle ABC then

sin space open parentheses fraction numerator straight B plus straight C over denominator 2 end fraction close parentheses

is equal to

$cos space straight B over 2$
$cos space straight C over 2$
$cos space straight A over 2$
$cos space straight A over 2$

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Short Answer Type

370. Prove the following identity:
2 (sin⁶θ + cos⁶θ) -3 (sin⁴θ + cos⁴θ) + 1 = 0

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