Question

show that cos sq 30−sin sq 30=(1−tan sq 30)÷1+tan squad 30​

Answer 1

Step-by-step explanation:

LHS= cos^2 30 - sin^2 30

= (root3/2)^2 - (1/2)^2

= 3/4 - 1/4

= 2/4

= 1/2

Now,

RHS = (1 - tan^2 30) / (1 + tan^2 30)

= 1 - ( 1/ root3)^2 / sec^2 30

= 1 - 1/3 / (2/ root3)^2

= (2/3)/ (4/3)

=2/3 * 3/4

=1/2

Hence, LHS=RHS proved.