Question

cos 21° - sin 21°/cos 21° + sin 21°= tan 24°​

Answer 1

Answer:

Step-by-step explanation:

We have,

\dfrac{\cos 21-\sin 21}{\cos 21+\sin 21}

Rationalising numerator and denominator, we get

=\dfrac{\cos 21-\sin 21}{\cos 21+\sin 21}\times \dfrac{\cos 21-\sin 21}{\cos 21-\sin 21}

=\dfrac{(\cos 21-\sin 21)^{2} }{\cos ^{2} 21-\sin ^{2} 21}

=\dfrac{(\cos^{2} 21+\sin^{2} 21)^{2}-2\sin 21\cos 21 }{\cos 2\times 21}

[ ∵ \cos ^{2} A-\sin ^{2} A}=\cos 2A]

=\dfrac{(1-\sin 2\times 21) }{\cos 42}

[∵\sin 2A=2\sin A\cos A]

=\sec 42-\tan 42

Hence, the value of\dfrac{\cos 21-\sin 21}{\cos 21+\sin 21} is \sec 42-\tan 42.

Answer 2

Step-by-step explanation:

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