Question

sec81 + cosec54,Express the given term of trigonometric ratios of angles having measure between 0 and 45.

Answer 1

SOLUTION :

Given :

Sec 81 + cosec 54

= sec (90 - 9) + cosec ( 90 - 36)

Sec 81 + cosec 54 = cosec 9 + sec 36

[ sec (90 - θ) = cosec 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.

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Answer 2

Given Sec 81 + Cosec 54

= Sec ( 90 - 9 ) + Cosec ( 90 - 36 )

= Cosec 9° + Sec 36°

[ ∵ Sec ( 90 - A ) = Cosec A ,

Cosec ( 90 - A ) = Sec A ]

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