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For x such that 0 < x < ⊼/2, the expression (√1-cos^2 x)/(sinx) + (√1-sin^2 x)/(cosx) is equivalent to:
trigonometry math trigonometry-identity
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for x such that 0 < x < ⊼/2, the expression (√1-cos2x)/(sinx) + (√1-sin2x)/(cosx)  is equivalent to:

a) 0

b) 1

c) 2

d) -tanx

e) sin2x

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judziy
Asked by judziyrep:909
University of Benin Nigeria
31 May 2020

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1 answer(s)

james_mark
James_mark answeredrep:231
School not set Nigeria
20 July 2020
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The answer is 2

EXPLANATION:

To solve this question, you need to know basic trigonometry:

sin2x + cos2x = 1

sin2x = 1 - cos2x ----------- eqn(1)

cos2x = 1  - sin2x ---------- eqn(2)

 (√1-cos2x)/(sinx) + (√1-sin2x)/(cosx)   ------------ eqn(1)

substituting eqn(1) and eqn(2) into eqn(3),

(√sin2x)/(sinx) + (√cos2x)/(cosx)

Also, √sin2x  = sinx, and √cos2x = cosx,

(sinx)/(sinx) + (cosx)/(cosx)

1 + 1 = 2

Ans C

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