AP EAMCET · Maths · Trigonometric Equations
\(\tan x+\frac{\cos x}{1+\sin x}=\)
- A \(\tan 2 x\)
- B \(\operatorname{cosec} x\)
- C \(\sec x\)
- D \(\cos 2 x\)
Answer & Solution
Correct Answer
(C) \(\sec x\)
Step-by-step Solution
Detailed explanation
\(\tan x+\frac{\cos x}{1+\sin x}\) \(\begin{aligned} & =\frac{\sin x}{\cos x}+\frac{\cos x}{1+\sin x} \\ & =\frac{\sin x+\sin ^2 x+\cos ^2 x}{\cos x(1+\sin x)} \\ & =\frac{(1+\sin x)}{\cos x(1+\sin x)}=\frac{1}{\cos x}=\sec x\end{aligned}\)
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