Question

How to solve this :') please help

Answer 1

3/2

Explanation:

sin(3π/4 - β) = sin(3π/4)cosβ - cos(3π/4)sinπ =

`\sin((3\pi)/(4)-\beta)=\sin((3\pi)/(4))\cos\beta-\cos(3\pi)/(4)\sin\beta\\=(1)/(√(2))\cos\beta-(-(1)/(√(2)))\sin\beta\\\\=(1)/(√(2))(\cos\beta +\sin\beta)\\\\\sin^2((3\pi)/(4)-\beta)=(1)/(2)\cos\beta +\sin\beta)^2=(1)/(2)(\cos^2\beta +\sin^2\beta+2\sin\beta\cos\beta\\=(1)/(2)(1+\sin2\beta)=(1)/(2)(1-(1)/(5)) = (2)/(5)\\`

Use
`\cot^2x=\csc^2x-1=(1)/(\sin^2x)-1`

so

`\cot^2((3\pi)/(4)-\beta)=(1)/(\sin^2((3\pi)/(4)-\beta))-1 = (1)/((2)/(5))-1=(5)/(2)-1=(3)/(2)`