Q3 of 23 Page 1

Solve any three sub-questions:

If sec then find the value of where is in IV quadrant.

sec α = -2 / √3

As α is in IV quadrant


∴ α is a negative acute angle


∴ X is positive & y is negative


∴ Cos α and sec α are positive


We know the identity that,


sec2 α – tan2 α = 1


sec2 α -1 = tan2 α





tan α = -1 / √3 ……………. (as α is in 4th quadrant)


cot α = -√3


We know the identity that,


cosec2 α – cot2 α = 1


cosec2 α = 1 + cot2 α


= 1 + (-√3)2


= 1 + 3


cosec2 α = 4


∴ cosec α = -2 …………………… (as α is in 4th quadrant)


1-cosec α = 1 – (-2)


= 1 + 2


1-cosec α = 3


1+cosec α = 1 + (-2)


= 1 – 2


1+cosec α = -1



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