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Question

cos² a + cos²(a-pi/2)

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Answer 1 · 2018-05-06T12:51:53

#1#

Since

#cos(alpha-pi/2)=sin(alpha)#, we have

#cos^2(a)+cos^2(alpha-pi/2) = cos^2(alpha)+sin^2(alpha)#

Finally, the fundamental rule of trigonometry states exactly that, for everty angle #alpha#, we have

#cos^2(alpha)+sin^2(alpha) = 1#

Answer 2 · 2018-05-06T19:04:44

# cos ^2 a + cos^2(a-pi/2) = 1#

# x = cos ^2 a + cos^2(a-pi/2)#

Cosine is even, #cos a = cos(-a)#

# x = cos ^2 a + cos^2(pi/2 - a)#

The cosine of the complementary angle is the sine of the original angle, #cos(pi/2-a)=sin a#.

# x = cos ^2 a + sin^2 a#

That's the Trig Pythagorean Theorem.

#x = 1#