Question

If
sin 990° sin 780° sin 390°
+
=K(tan 405° – tan 360°) then Ki
cos 540°cos 750°
cos 780°​

Answer 1

Answer:

I don't understand...

Answer 2

Given :   sin 990° sin 780° sin 390°  + cos 540°cos 750°cos 780°​  = K(tan 405° – tan 360°)

To find : value of K

Solution:

sin 990° sin 780° sin 390°  + cos 540°cos 750°

cos 780°​  = K(tan 405° – tan 360°)

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

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

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

sin 990° sin 780° sin 390°   = (-1)(√3 / 2)(1/2) = -√3 / 4

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

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

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

cos 540°cos 750°

cos 780°​   = (-1)(√3 / 2)(1/2) = -√3 / 4

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

tan  360° = 0

-√3 / 4 +   (-√3 / 4)  = k ( 1 - 0)

=> k = -√3/2

Value of k is -√3/2

if

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

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

=> 3 = k

Then k = 3

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