Question

if tantheta=20/21,show that 1-sintheta+costheta/1+sintheta+costheta=3/7.​

Answer 1

✯Given:-

• Tan θ = 20/21

✯To prove:-

• 1-sinθ+cosθ/1+sinθ+cosθ=3/7.

✯Proof:-

Formula's used:

⋆ sec²θ - tan²θ = 1

⋆ sin²θ +cos²θ = 1

⋆ cosθ = 1/secθ

Therefore,

→1+tan²θ =sec²θ

Given that tanθ = 20/21

⇒ 1 + (20/21)² = sec²θ

⇒ 1+400/441 = sec²θ

⇒ 441 + 400 /441 = sec²θ

⇒ 841 / 441 =sec²θ

⇒ sec θ = 29/21

Hence,

cosθ  = 21/29

Now,substituiting cosθ in the 2nd formula,

→ sin²θ +cos²θ = 1

⇒ sin²θ  = 1 - cos²θ

⇒ sin²θ = 1 - (21/29)²

⇒ sin²θ = 1 - 441/841

⇒ sin²θ  = 841 - 441 /841

⇒ sin²θ = 400/841

⇒ sinθ = 20/29

We have now found out the values of cosθ &sinθ .

Substituting these values in the given equation:

⇒ (1-sinθ+cosθ)÷(1+sinθ+cosθ)

⇒ [1-(20/29)+(21/29)]÷[1+(20/29)+(21/29)]

⇒ (1 + 1/29 )÷(1+41/29)

⇒ (30/29) ÷ (70/29)

⇒ 30 / 70

⇒ 3/7

Hence proved!

_____________

Answer 2

Answer:

3/7 is ur answer

hope you have understood the answer