Question

Express each one of the following in terms of trigonometric ratios of angles lying between 0° and 45°
(v)cosec 54° + sin 72°
(vi)cot 85° + cos 75°
(vii)sin 67° + cos 75°

Answer 1

(v) SOLUTION :  

Given : cosec 54° + sin 72°

cosec 54° + sin 72° = cosec (90° - 36°) + sin (90° - 18°)

= sec 36° + Cos 18°

[ cosec (90 - θ) = secθ ,sin (90 - θ) = cos θ , ]

Hence, cosec 54° + sin 72° = sec 36° + Cos 18°.

(vi) SOLUTION :  

Given : cot 85° + cos 75°

cot 85° + cos 75° = cot (90° - 5°) + cos (90° - 15°)

= tan 5° + sin 15°

[cot (90 - θ) = tan θ, cos (90 - θ) = sin θ ]

Hence, cot 85° + cos 75° = tan 5° + sin 15°

(vii) SOLUTION :  

Given : sin 67° + cos 75°

sin 67° + cos 75° = sin (90° - 23°) + cos (90° - 15°)

= cos 23° + sin 15°  

[sin (90 -  θ) = cos  θ , cos (90 - θ) = sin θ]

Hence, sin 67° + cos 75° = cos 23° + sin 15°  

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

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expression are as follows:-

(v) cosec 54° + sin 72°
= cosec(90°- 36°)+ sin (90°-18°)
= sec 36°+sin 18°

(vi)cot 85°+ cos 75°
= cot (90° -5°)+ cos (90°-15°)
= tan 5°+ cos 15°

(vii) sin 67°+ cos 75°
= sin (90°-23°)+ cos (90°-15°)
= cos 23°+ sin 15°

hope it helps you ✔✔✌✌⭐☺⭐⭐☺