Sin^2 (45+A) + sin^2 (45-A) = 1 prove

Question

Alondra Blackburn

Mathematics

15 October, 14:28

Sin^2 (45+A) + sin^2 (45-A) = 1 prove

+1

Answers (2)

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Addisyn Pittman · Answer 1

Step-by-step explanation:

We know that sinA=cos (90-A)

and, sin²A + cos²A = 1

Now, here sin (45+A) = cos {90 - (45+A) }

= cos (45-A)

cos² (45-A) + sin² (45-A) = 1

by Applying (sin²A + cos²A = 1)

Arjun Collins · Answer 2

sin (45+w) = sin (45) cos (a) + cos (45) sin (a)

sin (45-a) = sin (45) cos (a) - cos (45) sin (a)

sin2 (45+a) = sin2 (45) cos2 (a) + 2sin (45) cos (a) cos (45) sin (a) + cos2 (45) sin2 (a)

sin2 (45+a) = sina (45) cosa (w) - 2sin (45) cos (a) cos (45) sin (a) + cos2 (45) sin2 (a)

sin2 (45+a) + sin2 (45-a) = 2sin2 (45) cos2 (a) + 2cos2 (45) sin2 (a)

sin (45) = cos (45) = (√2) / 2

sin2 (45) = cos2 (45) = (1/2)

sin2 (45+a) + sin2 (45-a) = 2 (1/2) cos2 (a) + 2 (1/2) sin2 (a)

sin2 (45+a) + sin2 (45-a) = cos2 (a) + sin2 (a) = 1