Question

if 5 cos theta + 12 cos theta = 30 then prove that tan theta = 12/5​

Answer 1

Step-by-step explanation:

I am using x in case of theta-------------->

so 5 cosx = 13-12 sinx

squaring on both sides we get,

25 cos²x = 169 + 144 sin²x - 312 sinx

in case of cos²x we substitute (1-sin²x), as sin²x + cos²x = 1

equation will be 169 sin²x - 312 sinx + 144 = 0

after using quadratic formula we get sinx = 312/338

so sinx = 12/13.

we have to prove tan X =12/5

to prove

sin X =12/13=p/h

means

perpendicular (p) = 12

hypotenuse(h) =13

By Pythagoras theorem ,

base = 5

tan X = p/b= 12/5

tan X =12/5 .

Hence proved

this is the real process.

Answer 2

Answer:

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