Question

If sin∅ + cos∅ = √2cos∅,(∅≠90°) then the value of tan∅ is a) √2-1. b) √2 + 2. c) √2. d) -√2 ​

Answer 1

Answer:

The answer is A.√2-1

Divide by cos phi

Answer 2

$tan\theta = \sqrt{2}-1$

Step-by-step explanation:

$sin\theta + cos\theta = \sqrt{2} cos\theta\\sin\theta = \sqrt{2} cos\theta -cos\theta\\sin\theta = cos\theta(\sqrt{2} -1)$

Dividing by $cos\theta$ on both sides, we get

$\frac{sin\theta}{cos\theta} = \frac{cos\theta}{cos\theta} \sqrt{2}-1$

$\frac{sin\theta}{cos\theta} = tan\theta$

$tan\theta = \sqrt{2}-1$

Option a)$\sqrt{2}-1$ is the answer.

To Learn More....

1. Sin theta by cot theta + cosec theta minus sin theta by cos theta minus cosec theta is equals to 2 prove that

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2. Sintheta -cos theta /sin theta +cos theta +sin theta +cos theta /sin theta -cos theta =2/2sin²theta -1

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