## Calculus 8th Edition

Published by Cengage

# Appendix D - Trigonometry - D Exercises - Page A32: 46

#### Answer

$(sinx+cosx)^{2}=1+sin2x$

#### Work Step by Step

Need to prove the identity $(sinx+cosx)^{2}=1+sin2x$ In order to prove this, take left side isolate. $(sinx+cosx)^{2}=sin^{2}x+cos^{2}x+2sinx cosx$ Since, $2sinx cosx= sin2x$, and $sin^{2}x+cos^{2}x=1$ Hence, $(sinx+cosx)^{2}=1+sin2x$

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