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values of sinQ10, in Δ。PQ, right-angled at P, OP-7cm and OQ-PQ = 1cm. Determine the valueand cosQProve that : sin':9 + cos"θ + 3sinag cosag!11y) |
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Answer» Consider, sin6ө+cos6ө =1-3sin2өcos2ө(sin2ө)3+(cos2ө)3= (sin2ө+cos2ө)3− 3 (sin2ө cos2ө)(sin2ө+cos2ө) [since a + b = (a+b)3− 3ab(a+b)] = 1 − 3sin2өcos2ө [Since sin2ө+cos2ө = 1] OPQ is rt angled at P .OP=7cmOQ-PQ=1cmso, OQ = 1 + PQBY PYTHAGORUS THEOREM,OQ^2=OP^2+PQ^2(1+PQ)^2= 7^2 + PQ^21 + PQ^2+2PQ= 49 + PQ^22PQ= 48PQ=24cmOQ= 25cm thanks |
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