Question
If (sinx + siny) = a and (cosx + cosy) = b, then find
the value of (sinx siny + cosx cosy). [A] (a²+b²-2)/ 2 [B] (a2-b2-2)/ 2 [C] (a²+b²-1)/ 2 [D](a²+b²+2)/2Solution
(sinx + siny) = a         (both sides squaring). a2 =sin2x +sin2y +2sinx.siny  … (1) (cosx + cosy) = b       (both sides squaring). b2 =cos2x +cos2y+2cosx.cosy            … (2) Now EQ (1) +EQ (2) … (sin2x +sin2y +2sinx.siny) + cos2x +cos2y+2cosx.cosy =a2+b2 =1+1+2(sinx. siny+cosx. cosy) = a2+b2 2(sinx. siny+cosx. Cosy) = a2+b2-2 sinx. siny+cosx. Cosy = (a2+b2-2)/2.
More Trigonometry Questions
32 X 25 ÷ 4 + 12 of 30 = ? X 5 - 30Â
Evaluate: 18 ÷ 3 × 4 + 6 − 5
25% of 250 + 32% of 200 = ? ÷ √ 16
15% of 1800 + 22 = ?Â
118 × 6 + 13 + 83 = ?
- What will come in the place of question mark (?) in the given expression?
35% of 400 - 20% of 300 = (? - 30) X 2 - What will come in place of the question mark (?) in the following questions?
120÷(5×2)+8=? √? = 32% of 900 + 48% of 50
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