InterviewSolution
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InterviewSolution
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If sec θ + tan θ =p, then find the value of sin θ interms of p. (R- |
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Answer» Given : secx + tanx = p ................................... (i)Now, we know that : sec²x - tan²x = 1or, (secx + tanx)(secx - tanx) = 1 Putting (i)in the equation, we get :-p(secx- tanx) = 1or, secx - tanx = 1/p .........................................(ii) Now adding (i) and (ii), we get :-secx + tanx + secx - tanx = 1/p + por, 2secx = (1+p²)/por, secx = (1+p²)/2p On subtracting (ii) from (i), we get :-(secx + tanx) - (secx - tanx) = p -1/por, 2tanx = (p² - 1)/por, tanx = (p² - 1)/2p [Ans 2] We know that sinx = sinx/cosx x cosxor, sinx = tanx x 1/secxor, sinx = tanx/secxor, sinx = [(p² - 1)/2p]/[(p²+1)/2p] ..(Inthe next step both the 2p get cancelled)or, sinx = (p²-1)/(p²+1) |
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