Question

Hey huys plz do complete the question given below

Answer 1

Solution :-

Before solving :-

• Sin²∅ + Cos²∅ = 1

• Cosec²∅ - Cot²∅ = 1

• Sec²∅ - Tan²∅ = 1

• Tan(90 - x) = Cot(x)

• Sin(90 - x) = Cos(x)

• Cos(90 - x) = Sin(x)

• Sec(90 - x) = Cosec(x)

• Cosec(90 - x) = Sec(x)

• Cot(90 - x) = Tan(x)

Now coming back to the question :-

$= \sqrt{\dfrac{2sin^2(38^{\circ}) + 3 + 2sin^2(52^{\circ})}{3cosec^2(17^{\circ}) -2 - 3tan^2(73^{\circ})} }$

$= \sqrt{\dfrac{2sin^2(38^{\circ}) + 3 + 2sin^2(90^{\circ} - 38^{\circ})}{3cosec^2(17^{\circ}) -2 - 3tan^2(90^{\circ} - 17^{\circ})}}$

$= \sqrt{\dfrac{2sin^2(38^{\circ}) + 3 + 2cos^2(38^{\circ})}{3cosec^2(17^{\circ}) -2 - 3cot^2(17^{\circ})} }$

$= \sqrt{\dfrac{2(sin^2(38^{\circ}) + cos^2(38^{\circ}) )+ 3}{3(cosec^2(17^{\circ}) - cot^2(17^{\circ}))-2}}$

$= \sqrt{\dfrac{2(1)+ 3 }{3(1) -2 }}$

$= \sqrt{\dfrac{2+ 3 }{3 -2 }}$

$= \sqrt{\dfrac{5}{1 }}$

$=\sqrt{5}$