Prove that $\dfrac{\tan x}{1+\sec x}+\dfrac{1+\sec x}{\tan x}=2\cosec x$.[4] Hence, solve \(\

Question

Prove that $\dfrac{\tan x}{1+\sec x}+\dfrac{1+\sec x}{\tan x}=2\cosec x$.[4] Hence, solve $\dfrac{\tan 2x}{1+\sec 2x}+\dfrac{1+\sec 2x}{\tan 2x}=3\sec x$ for $-\pi \leq x \leq \pi$.[4] Use the result in part (a) to find the range of values of $k$ for which the equation $ \dfrac{\tan x}{1+\sec x}+\dfrac{1+\sec x}{\tan x}=k $ has no solutions. [2]

Accepted Answer

(b) $x=0.340\text{ rad}$ or $2.80\text{ rad}$ (c) $-2\le k\le2$

2025 CGSS PRELIMS P1 Q11

2025 CGSS PRELIMS P1 Q11

Solution:

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