Question

if sinxcos(pi/7)-sin(pi/7)cosx=-sqrt2/2 then x can equal?

Answer 1

Answer:

hope this help

Step-by-step explanation:

Answer 2

The requires value of x is -3pi/28.

What are trigonometric identities?

Trigonometric identities are the equalities that involve trigonometry functions and holds true for all the values of variables given in the equation.

It is given that-

sinxcos(pi/7) - sin(pi/7)cosx = -sqrt2/2

This can be written as-

sinxcos(pi/7) - sin(pi/7)cosx = -1/sqrt2

since sin(-pi/4) = -1/sqrt2

sinxcos(pi/7) - sin(pi/7)cosx =  sin(-pi/4)

Using the trigonometry identity,

sinAcosB - cosAsinB = sin(A - B)

The given equation can be written as-

sin(x - pi/7) =  sin(-pi/4)

⇒ x - pi/7 = -pi/4

⇒ x  = -pi/4 + pi/7

⇒ x  = -pi/4 + pi/7

⇒ x  = -3pi/28

Hence,the required value of x is -3pi/28.

More about trigonometry identity:

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