Question
If a tan θ = b, then a cos 2θ + b sin 2θ =
Answer: Option A
:
A
Given that tan θ = ba.
Now, a cos 2θ + b sin 2 θ = a(1−tan2θ1+tan2θ) + b(2tanθ1+tan2θ)
Putting tanθ = ba, we get
= a⎛⎝1−b2a21+b2a2⎞⎠ + b⎛⎝2ba1+b2a2⎞⎠ = a(a2−b2a2+b2) + b(2baa2+b2)
= 1(a2+b2) a3−ab2+2ab2 = a(a2+b2)a2+b2 = a.
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:
A
Given that tan θ = ba.
Now, a cos 2θ + b sin 2 θ = a(1−tan2θ1+tan2θ) + b(2tanθ1+tan2θ)
Putting tanθ = ba, we get
= a⎛⎝1−b2a21+b2a2⎞⎠ + b⎛⎝2ba1+b2a2⎞⎠ = a(a2−b2a2+b2) + b(2baa2+b2)
= 1(a2+b2) a3−ab2+2ab2 = a(a2+b2)a2+b2 = a.
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