Question

prove that sin square theta + cos square theta is equal to 1​

Answer 1

To prove:

sin²x+cos²x=1

Proof 1:

Refer to attachment 1

When x=60°,

sin²60+cos²60

=(1/2)²+(√3/2)²

=1/4+3/4

=4/4

=1

When x=0°,

sin²0+cos²0

=1+0

=1

This is true for all values of sin x and cos x.

Hence,proved

Proof 2:

Refer to attachment 2

Now,

sin x=AB/BC→sin²x=AB²/AC².......................(1)

cos x=AC/BC→cos²x=BC²/AC².........................(2)

Adding (1) and (2),

sin²x+cos²x

=AB²/AC²+BC²/AC²

=(AB²+BC²)/AC²

=AC²/AC²

=1

Hence,proved.

Here,

AB is the perpendicular,AC is the hypotenuse and BC is the base

Now,

In a right triangle,

Hypotenuse ²=Base²+Perpendicular ²

→AC²=AB²+BC²