InterviewSolution
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If cos x = -3/5 and π < x < 3π/2 find the values of other five trigonometric functions and hence evaluate (cosec x + cot x)/(sec x - tan x) |
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Answer» Given as cos x = -3/5 and π < x < 3π/2 As we know that in the third quadrant, tan x and cot x are positive and all other rations are negative. On using the formulas, Sin x = – √(1 - cos2 x) Tan x = sin x/cos x Cot x = 1/tan x Sec x = 1/cos x Cosec x = 1/sin x Then, Sin x = – √(1 - cos2 x) = – √(1 - (-3/5)2) = – √(1 - 9/25) = – √((25 - 9)/25) = – √(16/25) = – 4/5 Tan x = sin x/cos x = (-4/5)/(-3/5) = -4/5 × -5/3 = 4/3 Cot x = 1/tan x = 1/(4/3) = 3/4 Sec x = 1/cos x = 1/(-3/5) = -5/3 Cosec x = 1/sin x = 1/(-4/5) = -5/4 ∴ (cosec x + cot x)/(sec x - tan x) = [(-5 + 3)/4]/[(-5 - 4)/3] = [-2/4]/[-9/3] = [-1/2]/[-3] = 1/6 |
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