How do you use the sum to product formulas to write the sum or difference #cos(theta+pi/2)-cos(theta-pi/2)# as a product?

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Answer 1 · 2017-03-03T16:53:54

#-2sin theta.#

We know that, #cos A- cos B=-2sin ((A+B)/2)sin ((A-B)/2).#

Here, we have, #A=theta+pi/2, and, B=theta-pi/2.#

#:. (A+B)/2=1/2{(theta+pi/2)+(theta-pi/2)}=theta,# and,

#(A-B)/2=1/2{(theta+pi/2)-(theta-pi/2)}=pi/2.#

#rArr"The Expression="-2(sin theta)(sin(pi/2))=-2sintheta.#

Alternatively,

#cos(theta+pi/2)=-sintheta, and, cos(theta-pi/2)=sintheta,# hence,

#"The Exp.="-sintheta-sintheta=-2sintheta,# as before!

Enjoy Maths.!