TS EAMCET · Maths · Trigonometric Equations
The general solution of the equation \(\sqrt{6-5 \cos x+7 \sin ^2 x}-\cos x=0\) also satisfies the equation
- A \(\tan x+\cot x=2\)
- B \(\cot x+\operatorname{cosec} x=1\)
- C \(\tan x+\sec x=1\)
- D \(\sec x+\operatorname{cosec} x=2\)
Answer & Solution
Correct Answer
(C) \(\tan x+\sec x=1\)
Step-by-step Solution
Detailed explanation
\(\sqrt{6-5 \cos x+7 \sin ^2 x}=\cos x\) (Condition: \(\cos x \ge 0\)) \(6-5 \cos x+7(1-\cos^2 x)=\cos^2 x\) \(8 \cos^2 x+5 \cos x-13=0\) \((8 \cos x+13)(\cos x-1)=0\) \(\cos x=1\) (since \(\cos x \ge 0\) and \(\cos x \ne -13/8\)) Check option C: \(\tan x+\sec x=1\)…
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