Question

The value of tan $\left(1^{∘}\right)+$ tan $\left(89^{∘}\right)$ is equal to

• A. $\frac{1}{\sin (1^{∘})}$
• B. $\frac{2}{\sin (2^{∘})}$
• C. $\frac{2}{\sin (1^{∘})}$
• D. $\frac{1}{\sin (2^{∘})}$
• E. $\frac{2}{\sin (2^{∘})}$

Answer 1

Answer: (B)

$\tan 1^{∘}+\tan 89^{∘}=\tan 1^{∘}+\tan \left(90^{∘}−1^{∘}\right)$
$=\tan 1^{∘}+\cot 1^{∘}=\frac{\sin 1^{∘}}{\cos 1^{∘}}+\frac{\cos 1^{∘}}{\sin 1^{∘}}$
$=\frac{{\sin }^2{1}^{∘}+{\cos }^2{1}^{∘}}{\sin 1^{∘}\cos 1^{∘}}$
$=\frac{2}{2\sin 1^{∘}\cos 1^{∘}}=\frac{2}{\sin 2^{∘}}$