Question

cos theta is greater than zero tan theta + sin theta equal to M and tan theta minus sin theta equal to 1 then show that x square minus n square equal to 4 root MN ​

Answer 1

Step-by-step explanation:

question is not clear, I am making my own corrections in the information and proving accordingly.

i am using A in place of theta

tanA + sinA = M

tanA - sinA = N

LHS = M^2 - N^2

= (tanA+sinA)^2 - (tanA-sinA)^2

= tan^2A + sin^2 A + 2tanAsinA - tan^2A - sin^2A + 2tanAsinA)

= 4tanAsinA

RHS = 4√MN

= 4√(tanA+sinA)(tanA-sinA)

= 4√(tan^2A - tanAsinA + tanAsinA - sin^2A)

= 4√ (tan^2A - sin^2A)

=4√(sin^2A/cos^2A - sin^2A)

= 4√sin^2A(1-cos^2A)/cos^2A

= 4√sin^2A*sin^2A/cos^2A

= 4√tan^2Asin^2A

= 4tanAsinA

hence, LHS = RHS

proved