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prove that (sinθ + cosecθ)^2 + (cosθ + secθ)^2=7+tan^2θ+cot^2θ
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Posted by jeew-m on September 23, 2012 at 5:15 PM (Answer #1)
The relation `(sin x + cosec x)^2 + (cos x + sec x)^2 = 7 + tan^2 x + cot^2x` has to be proved. (` theta` has been substituted with x)
Start with the left hand side:
`(sin x + cosec x)^2 + (cos x + sec x)^2`
=> `sin^2 x + cosec^2x + 2*sin x*cosec x + cos^2x + sec^2x + 2*cos x*sec x`
=> `1 + cosec^2x + 2 + sec^2x + 2`
=> `1 + 1 + cot^2x + 2 + 1 + tan^2x + 2`
=> `7 + cot^2x + tan^2x`
This proves that `(sin x + cosec x)^2 + (cos x + sec x)^2 = 7 + tan^2 x + cot^2x`
Posted by justaguide on September 23, 2012 at 5:25 PM (Answer #2)
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