Question

if sec theta = 5/4 find the value of cos² theta -sin² theta​

Answer 1

Answer:

Cos²∅-Sin²∅=1/25

Step-by-step explanation:

Sec∅=5/4

( sec∅ is the reciprocal of cos∅)

Cos∅=base/hypotenuse

Sec∅= hypotenuse/base

=5/4= h/b

Now

Let h=5x and b=4x

By Pythagoras Theorem,

H²=P²+B²

P²= H²-B²

P²=(5x)²-(4x)²

= 25x²-16x²

=9x²

Therefore, P=√9x

P=3x.

Now,

Sin∅=p/h =3x/5x=3/5

Cos∅=b/h=4x/5x=4/5

Therefore:

Cos²∅-Sin²∅= (4/5)²-(3/5)²

= 16/25 - 15/25

=1/25

Hope it helps you!