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4 November, 13:31

In ΔPQR, ∠P and ∠Q are complementary angles. if Sin Q=4/5, COS p+COS Q =

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  1. 4 November, 17:05
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    P + Q are complementary means that P+Q = 90°.

    Then R is a right angle, i. e. it measures 90°.

    In a right angle you can write:

    sen (90-x) = cos (x)

    cos (90-x) = sin (x)

    Then sin Q = 4/5 ⇒ cos (90-Q) = cos P = 4/5

    Now sin^2 (P) + cos^2 (P) = 1

    sin^2 (P) = 1 - cos^2 (P)

    sin^2 (P) = 1 - [4/5]^2 = 9/25

    sin (P) = 3/5

    cos (Q) = sin (P) = 3/5

    cos (P) + cos (Q) = 4/5 + 3/5 = 7/5
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