What's the product of (sin a +cos a)(sin a +cos a)?
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[tex] \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} [/tex]
/* By Algebraic Identity */
[tex] \boxed { \pink { sin^{2} A + cos^{2} A = 1 }} [/tex]
[tex]\blue { = 1 + sin2A }[/tex]
[tex] \boxed { \orange { Since, 2sinAcosA = sin 2A }}[/tex]
Therefore.,
[tex] \red{ Product \:of \:(sin A +cos A)(sin A +cos A) }\\\green { = 1 + 2sinAcosA} [/tex]
[tex] \green { = 1 + sin2A }[/tex]
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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:
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