Class 10 Maths Introduction to Trigonometry questions with solutions Trigonometry

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Solution

Q.
If sinθ + cosθ = $\sqrt{2}$ , then tanθ + cot θ =

1 1

2 2

3 3

4 4

Ans.
(2)

$\sin θ + \cos θ = \sqrt{2}$

Squaring on both sides, we get

$\sin^{2} θ + \cos^{2} θ + 2 \sin θ \cos θ = 2$

$\Rightarrow 1 + 2 \sin θ \cos θ = 2$ $[∵ \sin^{2} θ + \cos^{2} θ = 1]$

$\Rightarrow 2 \sin θ \cos θ = 1 \Rightarrow \sin θ \cos θ = \frac{1}{2}$

But $\tan θ + \cot θ = \frac{\sin θ}{\cos θ} + \frac{\cos θ}{\sin θ} = \frac{\sin^{2} θ + \cos^{2} θ}{\cos θ \sin θ} = 2$

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