AP EAMCET · Maths · Trigonometric Equations
If \(a \sin ^2 \theta+b \cos ^2 \theta=c\), then \(\tan ^2 \theta\) is equal to
- A \(\frac{b-c}{a-c}\)
- B \(\frac{c-b}{a-c}\)
- C \(\frac{a-c}{b-c}\)
- D \(\frac{a-c}{c-b}\)
Answer & Solution
Correct Answer
(B) \(\frac{c-b}{a-c}\)
Step-by-step Solution
Detailed explanation
\(a \sin ^2 \theta+b \cos ^2 \theta=c\) On dividing both sides by \(\cos ^2 \theta\) \(a \tan ^2 \theta+b=c \sec ^2 \theta\) \(\Rightarrow \quad a \tan ^2 \theta+b=c\left(1+\tan ^2 \theta\right)\) \(\Rightarrow \quad a \tan ^2 \theta+b=c+c \tan ^2 \theta\)…
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