Question

if sinx/siny =1/2. and cosx/cosy=3/2. Then find tan²(x +y) =???




Any one can solve?
I want answer with cmplte process... ​

Answer 1

Given : sinx/siny =1/2. and cosx/cosy=3/2.

To find : tan²(x +y)

Solution:

sinx/siny =1/2

=> siny = 2sinx

=> sin²y = 4sin²x

cosx/cosy=3/2

=> cosy = 2Cosx/3

=> cos²y = 4cos²x/9

sin²y  + cos²y =  1

=> 4sin²x  + 4cos²x/9  = 1

=> 36sin²x + 4cos²x  = 9

=>  36sin²x + 4 - 4sin²x  = 9

=> 32sin²x  = 5

=> sin²x  = 5 /32

sin²x  = 5 /32

cos²x = 27/32

=> tan²x = 5/27  => tanx = √5 / 3√3

sin²y = 5/8

cos²y  = 3/8

=>  tan²y = 5/3   => tany = √5 /√3

tan(x +y)   = (tanx  + tany )/(1 - tanxtany)

= (√5 / 3√3 + √5 /√3)/( 1 - (√5 / 3√3)(√5 /√3))

= ( 4√5/3√3)/(( 9- 5)/9)

= 9 *  4√5/ 3√3 * 4

= √3 √5

= √15

tan(x +y) = √15

tan²(x +y)  = 15

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