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
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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
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