if x is an acute angle and sin x=cos x find the value of 2sin^2x-3cos^2x+1/2 cot^2x
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Answer:
0
Step-by-step explanation:
Given,
Sin x = Cos x and x is acute angle.
=> x = 45° ( ∵ Sin45 = Cos45 = 1/√2)
Now,
2Sin²x - 3Cos²x + 1/2 Cot²x
= 2 * (Sin²45) - 3 (Cos²45) + 1/2(Cot²45)
= 2 * 1/2 - 3 * 1/2 + 1/2 * 1 (∵ sin45 = cos45 = 1/√2 and Cot45 = 1)
= 1 + 1/2 - 3/2
= 3/2 - 3/2
= 0
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