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02. cose + sido -p andSeco + coseco =q, Prove thatqCp21)=2p?4. Od |
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Answer» q(p^2-1) = 2p =>LHS = q(p^2-1) =>sec +cosec [(sin + cos)^2-1 => (sec+cosec) [sin^2+cos^2+2sin.cos -1] = >(1/cos +1/sin) [1+2sin.cos-1] {{identity: sin^2+cos^2=1}} taking LCM of 1/sin + 1/cos=> (sin+cos/sin.cos)[2sin.cos] = >sin + cos /sin.cos* 2sin.cos => 2(sin + cos) = >2(p) {{sin + cos = p :(given in question)}} Therefore 2p i.e. = RHS |
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