Question

value of x in,cos x - sin x/cos x - sin x= 1-root3/1+root 3​

Answer 1

Answer:

x=3π/4

Step-by-step explanation:

• cos x - sin x/cos x + sin x= 1-√3/1+√3
• (cos x - sin x/cos x + sin x)(cos x-sin x/cos x-sin x)

(1-√3/1+√3)(1-√3/1-√3)

• (cos x-sin x)²/(cos ²x-sin ²x)=(1-√3)²/(1-3)
• (cos x-sin x)²/(cos ²x-sin ²x)=(1+3-2√3)/2
• (cos x-sin x)²/(cos ²x-sin ²x)=(2-√3)
• {cos x-sin x}{cos x-sin x}/(cos x+sin x/cos x-sin x)

=(2-√3)

• {cos x-sin x}/(cos x+sin x)=(2-√3)
• {cos x-sin x}=(2-√3) cos x+(2-√3) sin x
• {cos x-sin x}=2 cos x+2 sin x-√3 cos x -√3 sin x
• -3cos x+√3 cos x=3 sin x-√3 sin x
• -√3 (√3cos x-cos x)=-√3(-√3 sin x+ sin x)
• (√3-1) cos x=-(√3-1) sin x
• cos x= - sin x
• cot x=-1
• x=3π/4