Question

What's the product of (sin a +cos a)(sin a +cos a)?

Answer 1

$\red{ Product \:of \:(sin A +cos A)(sin A +cos A) } \\= ( SinA + cos A )^{2} \\= sin^{2} A + cos^{2} A + 2sinAcosA \\\green {= 1 + 2sinAcosA}$

/* By Algebraic Identity */

$\boxed { \pink { sin^{2} A + cos^{2} A = 1 }}$

$\blue { = 1 + sin2A }$

$\boxed { \orange { Since, 2sinAcosA = sin 2A }}$

Therefore.,

$\red{ Product \:of \:(sin A +cos A)(sin A +cos A) }\\\green { = 1 + 2sinAcosA}$

$\green { = 1 + sin2A }$

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Answer 2

Answer:

1 + Sin 2a

Step-by-step explanation:

(sin a + cos a)(sin a + cos a)

= (sin a + cos a)^2

= sin^2 a + cos^2 a + 2(cos a)(sin a)

= 1 + sin 2a

Predefined results used above:

• sin^2 a + cos^2 a = 1
• 2(sin a)(cos a) = sin 2a

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