Question

 Prove the identity.

 cscx - sinx = cotx cosx

 Note that each Statement must be based on a Rule chosen from the Rule menu. To see a detailed description of a Rule, select the More Information Button 1 the right of the Rule.

 Prove the identity.

 Note that each Statement must be based on a Rule chosen from the Rule menu. To see a detailed description of a Rule, select the More Information Buttor the right of the Rule.

Answer 1

Answer 2

SOLUTION :

1.

LHS

= sc(x) - sin(x)

= 1/sin(x) - sin(x) 

= (1 - sin^2(x))/sin(x)

= cos^2(x)/sin(x)

= [ cos(x)/sin(x) ] cos(x)

= cot(x) cos(x) = RHS (PROVED)

2.

LHS

= cos(π+x) / cos(3π/2 -x) 

= cos(π+x) / sin(π/2 - (3π/2 - x))

= cos(π+x) / sin(- π + x)

= - cos(x) / (- sin(x))

= cot(x) = RHS (PROVED)