Question

(cos21-sin21)/(cos21+sin21)

Answer 1

(cos21-sin21)/(cos21+sin21)=(sin79-sin21)/(cos21+cos71)=sin58/cos90=sin58*sin0=0


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Answer 2

The value of $\dfrac{\cos 21-\sin 21}{\cos 21+\sin 21}$ is $\sec 42-\tan 42$.

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 $\sec 42-\tan 42$.