Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 5 - Trigonometric Identities - Section 5.4 Sum and Difference Identities for Sine and Tangent - 5.4 Exercises - Page 227: 26


$$\sin40^\circ\cos50^\circ+\cos40^\circ\sin 50^\circ=1$$

Work Step by Step

$$X=\sin40^\circ\cos50^\circ+\cos40^\circ\sin 50^\circ$$ From the identity of the sum of sines: $$\sin A\cos B+\cos A\sin B=\sin(A+B)$$ So here $X$ actually follows the above identity with $A=40^\circ$ and $B=50^\circ$. Therefore, $X$ can also be rewritten as $$X=\sin(40^\circ+50^\circ)$$ $$X=\sin90^\circ$$ $$X=1$$ In conclusion, $$\sin40^\circ\cos50^\circ+\cos40^\circ\sin 50^\circ=1$$
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