1.

In a right angled triangle if sinB = (5/13) then find the value of tanB + cosecB.​1). 151/652). 181/603). 191/754). None of these

Answer»

GIVEN sinB = (5/13) = Perpendicular/hypotenuse

⇒ We know that (Hypotenuse)2 = (Perpendicular)2 + (BASE)2

⇒ (13)2 = (5)2 + (Base)2

⇒ (Base)2 = (13)2 - (5)2

⇒ (Base)2 = 169 - 25

⇒ (Base)2 = 144

⇒ (Base) = √144

⇒ (Base) = 12

⇒ cosB = Base/hypotenuse = 12/13

⇒ tanB = SIN B/Cos B

⇒ tanB = (5/13)/(12/13)

⇒ tanB = 5/12

⇒ cosecB = (1/Sin B) = (13/5)

⇒ tanB + cosecB = (5/12) + (13/5)

⇒ (25 + 156)/60

⇒ 181/60

∴ Required value is 181/60


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