Is sin(x-(3pi)/2)+sin(pi/2+x)=2cos(x) ?

The answer to whether sin(x-(3pi)/2)+sin(pi/2+x)=2cos(x) is True

Popular >

prove sin(x-(3pi)/2)+sin(pi/2+x)=2cos(x)

prove

sin (x - \frac{3 π}{2}) + sin (\frac{π}{2} + x) = 2 cos (x)

True

Solution steps

sin (x - \frac{3 π}{2}) + sin (\frac{π}{2} + x) = 2 cos (x)

Manipulating left side

sin (x - \frac{3 π}{2}) + sin (\frac{π}{2} + x)

Rewrite using trig identities

= cos (x) + sin (\frac{π}{2} + x)

Rewrite using trig identities

= cos (x) + cos (x)

Add similar elements:

cos (x) + cos (x) = 2 cos (x)

= 2 cos (x)

We showed that the two sides could take the same form

\Rightarrow True

\frac{1}{cos ( x ) \cdot sin ( x )} - tan (x) = cot (x)

\frac{1}{csc ( x ) - 1} = sin (x) - 1

sec^{2} (x) cot^{2} (x) = csc^{2} (x)

sin (θ) + cot (θ) cos (θ) = csc (θ)

cot (θ) + tan (θ) = sec^{(2)} (θ) cot (θ)

Is sin(x-(3pi)/2)+sin(pi/2+x)=2cos(x) ?
The answer to whether sin(x-(3pi)/2)+sin(pi/2+x)=2cos(x) is True