Question

8sin theta=4+cos theta find the value of tan theta​

Answer 1

Answer:

⇒cosθ=45 or cosθ=−1213. If cosθ=45,sinθ=4+cosθ8=35⇒tanθ=34.

Answer 2

Answer:

0.75

Step-by-step explanation:

Given,

$8sin\beta = 4+cos\beta \\Squaring both sides,\\\(8sin\beta )^2 = (4 + cos\beta )^2\\or, 64sin^2\beta = 16 + 8cos\beta +cos^2\beta \\or, 64(1 - cos^2\beta ) = 16 + 8cos\beta +cos^2\beta \\or, 64 -64cos^2\beta= 16 + 8cos\beta +cos^2\beta\\or, 0=65cos^2\beta + 8cos\beta - 48\\or, 65cos^2\beta + 8cos\beta - 48=0\\or, 65cos^2\beta +60cos\beta-52cos\beta-48=0\\or, 5cos\beta(13cos\beta+12)-4(13cos/beta+12)=0\\or, (13cos\beta+12)(5cos\beta-4)=0\\Either,\\cos\beta+12=0[Rejected]$

$Or, \\5cos\beta-4=0\\cos\beta = \frac{4}{5} \\beta = 36.86\\\\Finally,\\tan/beta = tan36.86 = 0.75$