Question

If tan theta-cot theta=a and cos theta+sin theta=b,then show that (a2+4)(b2-1)2=4

Answer 1

Answer:

Step-by-step explanation:

Tanθ−cotθ=a

cosθ+sinθ=b

show that (a² + 4)(b² − 1)² = 4

(a² + 4) = (Tanθ−cotθ)² + 4  

=> tan²θ + cot²θ - 2tanθ.cotθ + 4

=>tan²θ + cot²θ - 2 + 4   (tanθ.cotθ = 1)

=>tan²θ + cot²θ +2  

=> (tan²θ + 1) + (cot²θ + 1)  

=> sec²θ + cosec²θ

=>1/cos²θ + 1/sin²θ  

=>sin²θ+cos²θ/cos²θ.sin²θ  

=>1/cos²θ.sin²θ

(b² − 1) = (cosθ+sinθ)² -1  

=> cos²θ + sec²θ +2cosθ sinθ -1

=> 1+2cosθ sinθ -1

=> 2cosθ sinθ

(b² − 1)² = (2cosθ sinθ)²

=>4cos²θ.sin²θ

(a² + 4)(b² − 1)²  

=> (1/cos²θ.sin²θ)(4cos²θ.sin²θ)

=. 1x4 = 4 (ANS)

Answer 2

Answer:

Step-by-step explanation: