Question

the value of sin theta
and cos (90-theta) are same​

Answer 1

Yes, the value of sinΘ and cos(90-Θ) are the same.

This is an identity

sinΘ=cos(90-Θ)

For example, let's say Θ is 30°

The value of sin30° is 1/2

The value of cos(90-Θ) = cos(90-30)

                                       = cos60°

                                      = 1/2

30 and 60 are the complimentary angles.

S0, sin30 = cos(90-30)

The inverse is also true.

That is, cosΘ=sin(90-Θ)

Answer 2

Given:

the value of sinΘ and cos(90-Θ) are the same.

The answer is "Yes" the value of sinΘ and cos(90-Θ) are the same. Because trigonometry is a relationship between the sides and angles of a triangle

we write Sin Theta = Cos (90 - Theta) and Cos Theta = Sin (90 - Theta).  

sinΘ=cos(90-Θ)

For example,

The value of sin30° is 1/2

The value of cos(90-Θ) = cos(90-30)

 = cos60°

 = 1/2

30 and 60 are the complimentary angles.

S0, sin30 = cos(90-30)

The inverse is also true.

Hence the the value of sin theta  and cos (90-theta) are same​