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Prove that: cos^2theta(1+tan^2theta)=1...

Prove that:
`cos^2theta(1+tan^2theta)=1`.

Text Solution

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LHS `=cos^2theta(1+tan^2theta)`
`=cos^2xxsec^2theta` …(`therefore 1 + tan^2theta = sec^2theta`)
`=(cos theta xx sex theta)^2`
`=1^2` ..(`therefore cos theta xx sec theta = 1`)
=1
=RHS
`therefore`LSH = RHS
`therefore cos^2theta(1+tan^2theta) = 1`.
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