Question
If 5 sinĪø + 3 cosĪø = 4 then value of 5 cosĪø - 3 sinĪø
= ?Solution
If 5 sinĪø + 3 cosĪø = 4 Let 5 cosĪø - 3 sinĪø = K Then squaring both equation and adding (5sinĪø+3cosĪø)^2 = (4)^2 (5cosĪø-3sinĪø)^2 = (K)^2 25 sinĀ²Īø + 9 cosĀ²Īø+ 30 sinĪø cosĪø = 16 ---------------------------------------------- 9 sinĀ²Īø + 25 cosĀ²Īø- 30 sinĪø cosĪø = KĀ² 34 sinĀ²Īø + 34 cosĀ²Īø = 16 + KĀ² 34 (sinĀ²Īø + 34 cosĀ²Īø) = 16 + KĀ² Ā Ā { sinĀ²Īø + cosĀ²Īø = 1} 34 = 16 + KĀ² KĀ² = 34 - 16 = 18 K = ā18 = Ā± 3ā2
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