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प्रश्न
Prove that `((1 - cos^2 θ)/cos θ)((1 - sin^2θ)/(sin θ)) = 1/(tan θ + cot θ)`
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उत्तर
LHS = `((1 - cos^2 θ)/cos θ)((1 - sin^2θ)/(sin θ))`
LHS = `(sin^2 θ/cos θ). (cos^2 θ/sin θ)`
LHS = sin θ. cos θ
RHS = `1/(tan θ + cot θ)`
RHS = `1/((sin^2 θ + cos^2 θ)/(sin θ. cos θ))`
RHS = `(sin θ. cos θ)/(sin^2 θ + cos^2 θ)`
RHS = sin θ. cos θ
LHS = RHS
Hence proved.
संबंधित प्रश्न
if `cosec theta - sin theta = a^3`, `sec theta - cos theta = b^3` prove that `a^2 b^2 (a^2 + b^2) = 1`
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`cosA/(1 + sinA) = secA - tanA`
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