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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°

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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

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

102 Views

Short Answer Type

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

L.H..S. = $space 2 left parenthesis sin to the power of 6 straight theta plus cos to the power of 6 straight theta right parenthesis space minus space 3 left parenthesis sin to the power of 4 straight theta plus cos to the power of 4 straight theta right parenthesis plus 1$
$equals 2 left square bracket left parenthesis sin squared straight theta right parenthesis cubed plus left parenthesis cos squared straight theta right parenthesis cubed right square bracket minus 3 left square bracket left parenthesis sin squared straight theta right parenthesis squared plus left parenthesis cos squared straight theta right parenthesis squared right square bracket plus 1 equals 2 left square bracket left parenthesis sin squared straight theta plus cos squared straight theta right parenthesis space minus space 3 space sin squared straight theta. space cos squared straight theta right square bracket space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space minus 3 left square bracket left parenthesis sin squared straight theta plus cos squared straight theta right square bracket squared equals space 2 left square bracket left parenthesis 1 right parenthesis cubed minus 3 sin squared straight theta. space cos squared straight theta right square bracket space minus 3 space left square bracket 1 minus 2 sin squared cos squared straight theta right square bracket plus 1 equals 2 space left parenthesis 1 minus 3 sin squared straight theta. space cos squared straight theta right parenthesis space minus 3 space left parenthesis 1 minus 2 sin squared cos squared straight theta right square bracket plus 1$