Question

If tan theta = 20/21 then (cos theta - sin theta)/(cos theta + sin theta) =


A 1/21


B 21/20


C 1/41


D 1/20

Pls answer me fast it's urgent

Answer 1

Step-by-step explanation:

correct answer is one upon 41 click the picture to see how I did it and please make me brainliest

Answer 2

Answer:

Option c

Step-by-step explanation:

♦ Given ♦ :-

• tan θ = 20/21

♦ To find ♦ :-

• The value of (cos θ-sin θ) /(cosθ+ sin θ)

♦ Solution ♦ :-

Given that tan θ = 20/21

On squaring both sides then

tan² θ = (20/21)²

=> tan² θ = 400/441

On adding 1 both sides then

=> tan² θ +1 = (400/441)+1

=> sec² θ = (400+441)/441

Since, sec² A - tan² A = 1

=> sec² θ = 841/441

=> sec θ = √(841/441)

=> sec θ = 29/21

=> 1/cos θ = 29/21

=> cos θ = 21/29

=> cos² θ = 441/841

=> 1-cos² θ = 1-(441/841)

=> sin² θ = (841-441)/841

Since, sin² A + cos² A = 1

=> sin² θ = 400/841

=> sin θ = √(400/841)

=> sin θ = 20/29

now,

cos θ - sin θ

= (21/29)-(20/29)

= (21-20)/29

= 1/29

cos θ+ sin θ

= (21/29)+(20/29)

= (21+20)/29

= 41/29

The value of (cos θ-sin θ) /(cosθ+ sin θ)

= (1/29)/(41/29)

= (1/29)×(29/41)

= 1/41

♦ Answer ♦ :-

The value of (cos θ-sin θ) /(cosθ+ sin θ) is 1/41

♦ Used Formulae ♦ :-

• sin² A + cos² A = 1
• sec² A - tan² A = 1
• sec A = 1/cos A