Question

prove that sin(150+x)+sin(150-x)=cosx

Answer 1

Answer:

Step-by-step explanation:

The given equation is:

$sin(150+x)+sin(150-x)=cosx$

Taking the Left hand side of the above equation, we get

LHS=$sin(150+x)+sin(150-x)$

LHS=$2sin(\frac{300}{2})cos(\frac{2x}{2})$

LHS=$2sin(150^{\circ})cosx$

LHS=$2sin(180^{\circ}-30^{\circ})cosx$

LHS=$2sin30^{\circ}cosx$

LHS=$2{\times}{\frac{1}{2}}cosx$

LHS=cosx

LHS=RHS

Hence proved

Answer 2

Solution:

LHS = sin(150+x)+sin(150-x)

=sin[90+(60+x)]+sin[90+(60-x)]

$\boxed {sin(90+A)=cosA}$

= cos(60+x)+cos(60-x)

$\boxed { cos(A+B)=cosAcosB-sinAsinB}$

=cos60cosx-sin60sinx+cos60cosx+sin60sinx

= cos60cosx+cos60cosx

= 2cos60cosx

= 2×(1/2)×cosx

= cosx

= RHS

Therefore,

sin(150+x)+sin(150-x)=cosx

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