Question

Given that *=5/12 what is the value of sin* +cos*

pls guys i need a quick answer​

Answer 1

±17/13

Explanation:

`sec^2x-tan^2 x=1\\sec^(2) x-((5)/(12) )^2=1\\sec^(2) x=1+(25)/(144) =(169)/(144)\\sec ~x=\pm(13)/(12) \\cos~x=\pm(12)/(13)\\x ~lies~in ~first~or~3rd~quadrant~as~tan~x>0\\if~ x~lies~ in~ 1st~ ,~then~ both sin~and~cos~are~positive.\\sin ~x=√(1-cos^2x) =\sqrt{1-((12)/(13))^2} =(5)/(13)\\sin~x+cos~x=(12)/(13)+(5)/(13)=(17)/(13)\\if ~x~lies~in~3rd~quadrant~then~both~are~negative.\\sin~x+cos~x=-(17)/(13)`