Question
If sinĪø +cos Īø = ā7/2, then find the value of sinĪø
ā cosĪø.Solution
sinĪø + cos Īø = ā7/2, Squaring both sides. ā sin2Īø + cos2Īø + 2sinĪø.cosĪø = 7/4 ā 1 + 2sinĪø.cosĪø = 7/4 ā sinĪø.cosĪø = 3/8 We can write; sin2Īø + cos2Īø = (sinĪø ā cosĪø)2 + 2sinĪø.cosĪø ā (sinĪø ā cosĪø)2 = 1 ā 3/4 = 1/4 ā (sinĪø ā cosĪø) = 1/2
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