Question

express 1+cos X in terms of sin

OR

what is the formula of 1+cosX?

Answer 1

Answer:

We know, sin²A + cos²A = 1

So,

→ sin²x + cos²x = 1

→ cos²x = 1 - sin²x

→ cosx = $\sqrt{1-sin^2 x}$

Hence,

→ 1 + cosx

→ 1 + $\sqrt{1-sin^2 x}$

Therefore 1 + cos can be written as 1 + $\sqrt{1-sin^2 x}$

Seems like your question needs correction.

If correct question is 1 + cos²x then from sin²x + cos²x = 1 we can write cos²x = 1 - sin²x

So, 1 + 1 - sin²x = 2 - sin²x

Answer 2

Answer:

We know, sin²A + cos²A = 1

So,

→ sin²x + cos²x = 1

→ cos²x = 1 - sin²x

→ cosx = \sqrt{1-sin^2 x}

1−sin

2

x

Hence,

→ 1 + cosx

→ 1 + \sqrt{1-sin^2 x}

1−sin

2

x

Therefore 1 + cos can be written as 1 + \sqrt{1-sin^2 x}

1−sin

2

x