Question

if sec theta minus tan theta divided / sec theta + tan theta = 1/4 find sin theta
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Answer 1

Answer:

sinø= 3/5

Step-by-step explanation:

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Answer 2

Answer:

sinβ = 1 or sinβ = 3/5.

Step-by-step explanation:

Given: $\frac{sec\beta-tan\beta}{sec\beta+tan\beta} = \frac{1}{4}$

⇒ $\frac{\frac{1}{cos\beta}-\frac{sin\beta}{cos\beta}}{\frac{1}{cos\beta}+\frac{sin\beta}{cos\beta}} = \frac{1}{4}$

⇒ $\frac{1-sin\beta}{1+sin\beta} = \frac{1}{4}$

On rationalizing L.H.S., we get

⇒ $\frac{(1-sin\beta)(1-sin\beta)}{(1+sin\beta)(1-sin\beta)} = \frac{1}{4}$

⇒ $\frac{1+sin^{2}\beta-2sin\beta }{1-sin^{2}\beta} = \frac{1}{4}$

⇒ $\frac{1+sin^{2}\beta-2sin\beta }{cos^{2}\beta} = \frac{1}{4}$

On cross multiplication, we get

⇒ 4(1 + sin²β - 2sinβ) = cos²β

⇒ 4 + 4sin²β - 8sinβ = cos²β

On adding sin²β both sides, we get

⇒ 4sin²β - 8sinβ + 4 + sin²β = cos²β+sin²β

⇒ 5sin²β - 8sinβ + 4 = 1

⇒ 5sin²β - 8sinβ + 3 = 0

⇒ sinβ = {8 ± √(64-4.3.5)} ÷ 5.2

⇒ sinβ = {8 ± √(64-60)} ÷ 10

⇒ sinβ = {8 ± √4} ÷ 10

⇒ sinβ = {8 ± 2} ÷ 10

On taking (+) sign, we get

⇒ sinβ = {8 + 2} ÷ 10 = 10÷10

⇒ sinβ = 1

On taking (-) sign, we get

⇒ sinβ = {8 - 2} ÷ 10 = 6÷10

⇒ sinβ = 3/5

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