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Prove that : tan θ/(1 − cot θ) + cot θ/(1 − tan θ) = 1 + sec θ cosec θ
Prove that : (1 + 1/tan² θ)(1 + 1/cot² θ) = 1/(sin² θ – sin⁴ θ)
Prove the following trigonometric identity : (cos A – 2 cos³ A)/(2 sin³ A – sin A) = cot A
Assertion (A) : For an angle θ, sec θ = 1 ⇒ tan θ = 0. Reason (R) : sec² θ + tan² θ = 1.
If sin 3A = 1, then find the value of cos 2A – tan² 45°.
If (sec A + tan A) (1 – sin A) = k cos A, then find the value of k.
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