Question

Express each of the following in terms of trigonometric ratios of angles between 0° to 45° :

(i) tan 81° + cos 72°
(ii) cot 49° + cosec 87°.

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Answer 1

Question:-

➡ Express each of the following in terms of trigonometric ratios of angles between 0° to 45°

Solution:-

Question 1:-

tan(81°) + cos(72°)

= tan(90° - 9°) + cos(90° - 18°)

= cot(9°) + sin(18°) (Hence expressed in terms of T-Ratios of angles between 0° to 45°)

Question 2:-

cot(49°) + cosec(87°)

= cot(90° - 41°) + cosec(90° - 3°)

= tan(41°) + sec(3°) (Hence expressed in terms of T-Ratios of angles between 0° to 45°)

It's told to express in terms of T-Ratios of angles between 0° to 45°. I have used the complementary angle formulae in solving this problem.

Formulae Used:-

➡ tan(90° - x) = cot(x)

➡ cos(90° - x) = sin(x)

➡ cot(90° - x) = tan(x)

➡ cosec(90° - x) = sec(x)

Answer 2

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Question 1:-

$\tan(81) + \cos(72) \: \\= \tan(90 - 9) + \cos(90 - 18)$

$= \cot(9) + \sin(18)$

Question 2:-

$\cot(49) + \cosec(87) \\ = \cot(90 - 41) + \cosec(90 - 3)$

$= \tan(41) + \sec(3)$