WBJEE · Maths · Trigonometric Equations
Let \(\alpha\) and \(\beta\) be iwo distinct roots of \(a \cos \theta+b \sin \theta=c,\) where \(a, b, c\) are three
real constants and \(0 \in|0,2 \pi|\). Then, \(\alpha+\beta\) is also a root of the same equation, if
- A \(a+b=c\)
- B \(b+c=a\)
- C \(c+a=b\)
- D \(c=a\)
Answer & Solution
Correct Answer
(D) \(c=a\)
Step-by-step Solution
Detailed explanation
Given equation is \(a \cos \theta+b \sin \theta=c\) \(\Rightarrow a\left(\frac{1-\tan ^{2} \frac{\theta}{2}}{1+\tan ^{2} \frac{\theta}{2}}\right)+\frac{2 b \tan \frac{\theta}{2}}{1+\tan ^{2} \frac{\theta}{2}}=c\)…
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