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- Homework Statement
- if a = sinx+cosx and b=tanx+cotx, then the value of a(b^2-1)-2 is

- Homework Equations
- sin^2(x)+cos^2(x)

b^2-1= tan^2(x) + cot^2(x) + 2 -1

b^2-1= sin^2(x)/cos^2(x) +cos^2(x)/sin^2(x) -1

b^2-1=[sin^4(x) +cos^4(x)]/sin^2(x)cos^2(x) -1

b^2-1=[1-sin^2(x)cos^2(x)]/sin^2(x)cos^2(x) -1

a(b^2-1)=sinx+cosx {[1-sin^2(x)cos^2(x)]/sin^2(x)cos^2(x) -1 }

I am not able to go any further than this step to reach the answer

b^2-1= sin^2(x)/cos^2(x) +cos^2(x)/sin^2(x) -1

b^2-1=[sin^4(x) +cos^4(x)]/sin^2(x)cos^2(x) -1

b^2-1=[1-sin^2(x)cos^2(x)]/sin^2(x)cos^2(x) -1

a(b^2-1)=sinx+cosx {[1-sin^2(x)cos^2(x)]/sin^2(x)cos^2(x) -1 }

I am not able to go any further than this step to reach the answer

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