Question

5 sin theta=3 find sec theta-tan theta/sec thetea+tan theta

Answer 1

We have

5 sin theta =3

sin theta =3/5

cos theta =4/5. (by Pythagoras theorem)

sec theta = 1/cos = 5/4

tan theta = sin/cos = 3/4

sec theta + tan theta = 8/4 = 2

I hope it would be helpful...

Answer 2

Given :-

5 sin θ = 3

To find :-

(sec θ - tan θ) / ( sec θ + tan θ )

Solution :-

∵ 5 sin θ = 3

∴ sin θ = 3 / 5

now, using identity

cos²θ = 1 - sin²θ

cos²θ = 1 - (3/5)²

cos²θ = 16 / 25

cos θ = 4/5

so,

sec θ = 5 / 4

tan θ = 3 / 4

we have to find

• (sec θ - tan θ) / (sec θ + tan θ)

multiplying by secθ - tanθ in both  numerator and denominator

• (secθ-tanθ)(secθ-tanθ) / (secθ+tanθ)(secθ-tanθ)

• ( secθ - tanθ)² / (sec²θ - tan²θ )

using identity sec²α - tan²α = 1

• (secθ - tanθ)² / 1

putting values of sec θ and tan θ

• ( (5/4) - (3/4) )²

• ( 2 / 4 )²

• ( 1 / 2 )²

   →     1 / 4   ( Ans.)

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we could also get answer by directly putting values of sec θ and tanθ

→ ( secθ - tanθ ) / ( secθ + tanθ )

→  ((5/4) - (3/4)) / ((5/4) + (3/4))

→ (2 / 4) ÷ (8 / 4)

→ ( 1 / 2) * ( 1 / 2 )

→ 1 / 4  (Ans.)