if cot theata=12/5show that tan2theata-sin2theta=sin4thetasec2 theta
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Correct question:
If cotθ = 12/5 show that tan²θ - sin²θ = sin²θ × tan²θ
Not Using the given value of cotθ
Given,
We know that
tan²θ = sin²θ/cos²θ
Substituting
=sin²θ/cos²θ-sin²θ
= sin²θ - cos²θsin²θ/cos²θ
= sin²θ(1 - cos²θ)/cos²θ
= sin²θ×sin²θ/cos²θ
= sin²θ × tan²θ
Hence proved
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