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prove that( 1 -sin theta )÷(1 + sin theta) is equals to tan^2(pi by 4 -theta /2) in meritnation

prove that( 1 -sin theta )÷(1 + sin theta) is equals to tan^2(pi by 4 -theta /2) in meritnation

Grade:11

2 Answers

Waseem khan
33 Points
4 years ago
1-sinθ/1+sinθ1 can be written as sin²θ/2+cos²θ/2And sinθ can be written as 2sinθ/2cosθ/2So 1-sinθ/1+sinθ can be written as sin²θ/2+cos²θ/2-2sinθ/2cosθ/2 divide by sin²θ/2+cos²θ/2+2sinθ/2cosθ/2(cosθ/2-sinθ/2)²/(cosθ/2+sinθ/2)²Dividing by cosθ/2 in both side we will get (1-tanθ/2)²/
Waseem khan
33 Points
4 years ago
1-sinθ/1+sinθ1 can be written as sin²θ/2+cos²θ/2And sinθ can be written as 2sinθ/2cosθ/2So 1-sinθ/1+sinθ can be written as sin²θ/2+cos²θ/2-2sinθ/2cosθ/2 divide by sin²θ/2+cos²θ/2+2sinθ/2cosθ/2(cosθ/2-sinθ/2)²/(cosθ/2+sinθ/2)²Dividing by cosθ/2 in both side we will get (1-tanθ/2)²/ (1+tanθ/2)² it can be written as tan²(pi/4-theta/2)

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