Question

In ΔPQR, ∠P and ∠Q are complimentary angles. If sinQ = 4/5 , cosP + cosQ =

Answer 1

complimentary means

P + Q = 90

P = 90 - Q

Cos(p) = cos(90-Q) = sinQ = 4/5 ( given)

You can find CosQ from the triangle of Q

CosQ = sqrt(5^2 - 4^2)/5 = 3/5


Required = CosP + CosQ = 4/5 + 3/5 = 7/5

Answer 2

CosP +CosQ =
`(7)/(5)` .

Explanation:

Given : In ΔPQR, ∠P and ∠Q are complimentary angles. If sinQ = 4/5 .

To find : cosP + cosQ =

Solution : We have given that ∠P and ∠Q are complimentary angles.

P + Q = 90 .

Q = 90 - P.

Then sin( 90 -p ) =
`(4)/(5)` .

As we know that sin( 90 -p ) = CosP =
`(4)/(5)` .

We have SinQ =
`(4)/(5)` .

CosQ =
`\sqrt{1 - Sin^(2)Q }`

Plugging the value of SinQ

CosQ =
`\sqrt{1 - ((4)/(5)) ^(2) }`.

CosQ =
`\sqrt{1 - ((16)/(25))}`.

CosQ =
`\sqrt{(9)/(25) }`.

CosQ =
`(3)/(5)` .

CosP +CosQ =
`(4)/(5)` +
`(3)/(5)`.

CosP +CosQ =
`(7)/(5)` .

Therefore, CosP +CosQ =
`(7)/(5)` .