Question

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Answer 1

Answer:

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Answer 2

Given :  3Cosθ  = 5Sinθ

To find : Value of  (5Sinθ  - 2Sec³θ  + 2Cosθ)/(5Sinθ +2Sec³θ - 2Cosθ)

Solution:

3Cosθ  = 5Sinθ

=> tanθ  = 3/5

Sec²θ = 1 + Tan² θ  = 1 + (3/5)²   = 34/25

(5Sinθ  - 2Sec³θ  + 2Cosθ)/(5Sinθ +2Sec³θ - 2Cosθ)

= (3Cosθ  - 2Sec³θ  + 2Cosθ)/(3Cosθ +2Sec³θ - 2Cosθ)

= (5Cosθ  - 2Sec³θ)/(Cosθ +2Sec³θ)

Dividing numerator & denominator by Cosθ    ( 1/ Cosθ = Secθ)

= (5   - 2Sec⁴θ)/(1 +2Sec⁴θ)

= (5 - 2(34/25)²) /( 1 + 2(34/25)²)

= (  3125  - 2312) / ( 625 + 2312)

= 813/2937

= 271/979

(5Sinθ  - 2Sec³θ  + 2Cosθ)/(5Sinθ +2Sec³θ - 2Cosθ) = 271/979  

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