Question

cos89 + cosec87,Express the given term of trigonometric ratios of angles having measure between 0 and 45.

Answer 1

SOLUTION :

Given :

Cos 89 + cosec 87

= cos (90 - 1) + cosec ( 90 - 3)

Cos 89 + cosec 87 = sin 1 + sec 3

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

**Trigonometric ratios of complementary angles : sec (90 - θ) = cosec θ , cosec ( 90 - θ) = secθ , sin (90 - θ) = cos θ, cos ( 90 - θ) = sin θ ]

Two angles are said to be complementary if their sum is 90°.

θ and (90 - θ) are complementary angles for acute angle θ.

HOPE THIS ANSWER WILL HELP YOU..

Answer 2

Given Cos 89° + Cosec 87°

= Cos ( 90° - 1° ) + Cosec ( 90° - 3° )

= Sin 1° + Sec 3°

[ ∵ Cos ( 90° - A ) = Sin A ,

Cosec ( 90° - A ) = Sec A ]

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