Question

if tan theta is equal to 1 then find the value of theta and sin theta​

Answer 1

Answer:

theta is 45° and sin45°= 1/√2

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Answer 2

Answer:

Given,

Tan theta = 1

we know,

1 + tan^2 theta = sec^2 theta

so,

1 + 1^2 = sec^2 theta

2 = sec^2 theta

or,

sec theta = root 2

now,

sec theta = 1/cos theta

so, cos theta = 1 / root 2

We know,

Cos theta = 1/root 2 when theta = 45°

So, theta = 45° and sin theta = sin 45° = 1/root 2

I hope it's clear now :)

Though, this was the proper way to do it, there's also a very simple way :)

Since Tan theta = 1

theta = 45°

sin theta = sin 45° = 1/root 2

That's it:)