Question

when sin990/cos540+sin780/cos750+sin390/cos780=k(tan405-tan360) is defined,then k=

Answer 1

Step-by-step explanation:

use methods such as sin(A+B). or

Answer 2

Given :  sin990/cos540+sin780/cos750+sin390/cos780=k(tan405-tan360)  

To find : Value of k

Solution:

sin 990°  = Sin ( 3 * 360° - 90°) = - Sin 90° =  - 1

cos 540° = Cos (360°  + 180° ) = Cos  180° = -1

=> sin990°/cos540° = 1

Sin 780° = Sin (2 * 360° + 60°) = Sin 60°  = √3 / 2

Cos 750° = Cos (2 * 360° + 30°) = Cos 30°  = √3/ 2

=> Sin 780° / Cos 750° = 1

Sin 390° = Sin (360° + 30°) = Sin 30°  = 1/2

Cos 780° = Cos (2 * 360° + 60°) = Cos 60°  = 1/ 2

Sin 390°  / Cos 780°   = 1

tan 405° = tan ( 360°+ 45°) = tan 45° = 1

tan  360° = 0

=> 1 + 1 + 1 = k ( 1 - 0)

=> 3 = k

Value of k = 3

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