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if tantheta -cottheta =a and costheta +sintheta =b then 4b^2(2-b^2)​

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Answer:

= 4(1+sin2theta)²

Step-by-step explanation:

Given the equations

tantheta -cottheta =a... 1

costheta +sintheta =b .... 2

We are to find 4b^2(2-b^2)​

Squaring both sides of equation 2

(costheta +sintheta)^2 = b^2

cos^2theta + 2costheta sintheta + sin^2 theta = b^2

(cos^2theta+ sin^2 theta) + 2costheta sintheta = b^2

1 + 2costheta sintheta = b^2

1 + sin2theta = b^2

substitute

4b^2(2-b^2)​

= 4(1+sin2theta)(2-1+sin2theta)

4(1+sin2theta)(1+sin2theta)

= 4(1+sin2theta)²

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