WBJEE · Maths · Trigonometric Ratios & Identities
If \(\sin ^{2} \theta+3 \cos \theta=2,\) then \(\cos ^{3} \theta+\sec ^{3} \theta\) is equal out to
- A 1
- B 4
- C 9
- D 18
Answer & Solution
Correct Answer
(D) 18
Step-by-step Solution
Detailed explanation
Given, \(\sin ^{2} \theta+3 \cos \theta=2\) \(\begin{array}{lr}\Rightarrow & 1-\cos ^{2} \theta+3 \cos \theta=2 \\ \Rightarrow & \cos ^{2} \theta-3 \cos \theta+1=0\end{array}\) \(\Rightarrow \quad \cos \theta=\frac{3 \pm \sqrt{9-4}}{2}\) (by quadratic formula)…
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