Question

Find the value of (sin 11 + cos 11) / (sin 11 - cos 11).

Answer 1

Answer:

Solution:

RHS

\frac{\cos 11+\sin 11}{\cos 11-\sin 11}

Divide numerator and denominator by cos⁡11

Hence the equation becomes

\frac{1+\tan 11}{1-\tan 11} \ldots(1)

By formula,

\tan (A+B)=\frac{\tan A+\tan B}{1-\tan A \tan B}

Bringing eq(1) in the above form,

\frac{1+\tan 11}{1-\tan 11}=\frac{\tan 45+\tan 11}{1-(\tan 45)(\tan 11)}

\frac{\tan 45+\tan 11}{1-(\tan 45)(\tan 11)}=\tan (45+11)=\tan (56)

\begin{array}{l}{\tan 56=\tan (90-34)} \\ {\tan (90-\mathrm{A})=\cot \mathrm{A}}\end{array}

Hence \tan (90-34)=\cot 34= RHS

\bold{\frac{\cos 11+\sin 11}{\cos 11-\sin 11}=\tan 56 \text { or } \cot 34}

LHS = RHS

Hence proved.