please simplify that 8 th question
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heya here is ur solution
(1-cosx)(1+cosx)(1+cot²x)
since (a-b)(a+b) = a²-b²
thus
= (1-cos²x)(1+cot²x)
since sin²x+cos²x= 1
thus sin²x = 1-cos²x
= sin²x(1+cot²x)
= sin²x + (sinx cotx)²
= sin²x + (sinx cosx/sinx)²
= sin²x +cos²x
= 1
(1-cosx)(1+cosx)(1+cot²x)
since (a-b)(a+b) = a²-b²
thus
= (1-cos²x)(1+cot²x)
since sin²x+cos²x= 1
thus sin²x = 1-cos²x
= sin²x(1+cot²x)
= sin²x + (sinx cotx)²
= sin²x + (sinx cosx/sinx)²
= sin²x +cos²x
= 1
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