Question

prove sec^2-tan^2=1​

Answer 1

Hey

As we already know that

(hypotenuse)^2 = (opposite)^2 + (adjacent)^2

{ By pythagoreas theorem }

Divide by (adjacent)^2 on both sides

(hypotenuse)^2 / (adjacent)^2 = (opposite)^2 / (adjacent)^2 + (adjacent)^2 / (adjacent)^2

Sec^2 = 1 + tan^2

sec^2 - tan^2 = 1

Hence proved

Answer 2

Answer:

Step-by-step explanation:

Explanation:

Left Hand Side::                         cos2means cos square x

sec 2 ( x ) − tan 2 x

= 1 cos 2 x − sin 2 x cos 2 x

= 1 − sin 2 x cos 2 x

= cos 2 x cos 2 x -> Use Property  

sin 2 x + cos 2 x

= 1  and isolate  cos 2 x

= cos 2 x cos 2 x

 = 1

 =  Right Hand Sid