Question

if sinx+siny=1/4, cosx+cosy=1/3 then show that cot (x+y)=7/24​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Given If sinx + siny = 1/4, cosx + cosy = 1/3 then show that cot (x+y) = 7/24

• Given sinx + siny = ¼
• So we have sina + sinb = 2 sin (a + b / 2) cos (a – b / 2)
•         cosa + cosb = 2 cos (a + b / 2)cos (a – b / 2)
•  Now sinx + siny = ¼
•     So 2 sin(x + y / 2) cos (x – y / 2) = ¼ ---------1
•      So cosx + cosy = 1/3
•           2 cos (x + y / 2)cos (x – y / 2) = 1/3-------2
•     Equation 1 divided by 2 will be
•    2 sin(x + y / 2) cos (x – y / 2) = ¼ /
•     2 cos (x + y / 2)cos (x – y / 2) = 1/3
•        tan (x + y / 2) = ¼ x 3/1
•                  tan(x + y/2) = ¾
• Now we can write tan(x + y) as tan 2 (x + y / 2)
•                                                             = 2 tan (x + y / 2) / 1 – tan^2 (x + y / 2)
•                                                               = 2(3/4) / 1 – (3/4)^2
•                                                                  = 3/2 / 16 – 9 / 16
•                                                                 = 3/2 x 16 / 7
•                                                     tan(x + y) = 24 / 7
•                           Now we have cot (x + y) = 1/ tan(x + y)
•                                                                     = 1/24/7
•                                                                     = 7/24

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https://brainly.in/question/7988636