Question

If 2sin theta+1=0 and 90°270° calculate a) 4cos²theta. b) 81tan²theta​

Answer 1

A)
`4\cos^2\theta=3`

B)
`81\tan^2\theta=27`

Explanation:

`\displaystyle 2\sin\theta+1=0;\:90^\circ \leq\theta\leq 270^\circ\\\\2\sin\theta=1\\\\\sin\theta=(1)/(2)\\ \\\theta=(5\pi)/(6)`

`\displaystyle 4\cos^2\theta=4\cos^2\biggr((5\pi)/(6)\biggr)=4\biggr(-(√(3))/(2)\biggr)^2=4\biggr((3)/(4)\biggr)=3`

`\displaystyle 81\tan^2\theta=81\tan^2\biggr((5\pi)/(6)\biggr)=81\biggr(-(√(3))/(3)\biggr)^2=81\biggr((3)/(9)\biggr)=81\biggr((1)/(3)\biggr)=(81)/(3)=27`