Question

prove that tan(45-theta)=cos theta -sin theta whole divided by cos theta +sin theta​

Answer 1

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Formula=Tan(A-B)= $\large{\frac{TanA-TanB}{1+TanATanB}}$

$\implies$ Tan(45-$\theta$)=$\large\frac{Tan45°-Tan\theta}{1+Tan45°Tan\theta}$

$\implies$ $\huge\frac{1-\frac{sin\theta}{cos\theta}}{1+1 \times \frac{sin\theta}{cos\theta}}$

$\implies$ $\frac{\dfrac{cos\theta-sin\theta}{cos\theta}}{\dfrac{cos\theta + sin\theta}{cos\theta}}$

$\implies$ $\large{\boxed{\boxed{\frac{cos\theta-sin\theta}{cos\theta+sin\theta}}}}$

Answer 2

Refer to attachment..

$\huge{\underline{\mathbb{\pink{Thankyou}}}}$