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1/cosec^2(51°)+sin^2(39°)+tan^2(51°)-1/sin^2(51°)sec^2(39°)
Transform the expression using:
1/cosec(x)=sin(x)
sin(90°-x)=cos(x)
1/cos(x)=sec(x)
cos^2(39°)+sin^2(39°)+tan^2(51°)-1
Use, sin^2(x)+cos^2(x)=1
1+tan^2(51°)-1
tan^2(51°)
cot^2(39°)
Use, cosec^2(x)-cot^2(x)=1
cosec^2(39°)-1
x^2-1
So the answer is x^2-1
Transform the expression using:
1/cosec(x)=sin(x)
sin(90°-x)=cos(x)
1/cos(x)=sec(x)
cos^2(39°)+sin^2(39°)+tan^2(51°)-1
Use, sin^2(x)+cos^2(x)=1
1+tan^2(51°)-1
tan^2(51°)
cot^2(39°)
Use, cosec^2(x)-cot^2(x)=1
cosec^2(39°)-1
x^2-1
So the answer is x^2-1
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