Verify each Identify 1 cot x sec x sin x 1 2 csc x csc x c

Verify each Identify. 1) cot x sec x sin x = 1 2) csc x - csc x cos^2 x = sin x 3) cos^2 theta (1 + tan^2 theta) = 1 4) tan theta + cot theta = sec theta csc theta

Solution

3).

given

cos^2(1+tan^2)=1

to prove this ,take left hand side(L.H.S)

L.H.S= cos^2(1+tan^2)

= cos^2(sec^2) [ since sec^2 - tan^2=1]

= cos^2/cos^2

=1

L.H.S=R.H.S

hence proved