If cosx/(1 - sinx) + cosx/(1+ sinx) = 4, 0° < x < 90°, then find the value of (tanx + cosecx).
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Correct answer: D
Explanation
Has been given :
cosx/(1 − sinx) + cosx/(1 + sinx) = 4 , 0° < x < 90°
According to the formula:
1 − sin²x = cos²x
cosx/(1 − sinx) + cosx/(1 + sinx)
= cosx[(1 + sinx + 1 − sinx) / (1 − sin²x)]
= cosx(2 / cos²x)
= 2 / cosx
2 / cosx = 4
cosx = 1/2
sinx = √(1 − cos²x)
= √(1 − 1/4)
= √(3/4)
= √3 / 2
tanx = sinx / cosx
= (√3/2) / (1/2)
= √3
cosecx = 1 / sinx
= 2 / √3
tanx + cosecx = √3 + 2/√3
= (3 + 2) / √3
= 5/√3
= 5√3 / 3