Question

IF TAN A+ SEC A=3 SO WHAT IS THE VALUE OF SIN A

Answer 1

heya!!

refer to given attachment please

Answer 2

Since we have to find the value of sinA, we have to convert the equation in terms of sinA.

We have,
tanA + secA = 3

⇒ sinA/cosA + 1/cosA = 3

⇒ (sinA + 1)/cosA = 3

⇒ (sinA + 1) = 3 cosA

⇒ sinA + 1 = 3 √(1-sin²A)

⇒ (sinA + 1)² = 9 (1 - sin²A)

⇒ sin²A + 2sinA + 1 = 9 - 9sin²A

⇒ 10sin²A + 2 sinA -8 = 0

⇒ 5 sin²A + sinA -4 = 0

⇒ 5sin²A + 5sinA -4sinA -4 = 0

⇒ 5sinA(sinA +1) - 4(sinA + 1) = 0

⇒ (5sinA -4)(sinA+1) = 0

∴ Either,
5sinA - 4 = 0 or sinA +1 = 0
sinA = 4/5 or sinA = -1