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Integration of Piecewise Continuous Functions

If α , β ar...

Question

If $α, β$ are complementary angles and $sin α = \frac{p}{q}$ , then $cos β =$

A

\frac{p}{q}

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B

\frac{q}{p}

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C

q

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D

\sqrt{q^{2} - p^{2}}

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Solution

The correct option is A $\frac{p}{q}$
$c o s β = cos (π / 2 - α) = sin α = p / q [A]$

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cos (α - β) + cos (β - γ) + cos (γ - α) = - \frac{3}{2}, cos α + cos β + cos γ = p & sin α + sin β + sin γ = q

α

α

= Q, then the value of

\frac{1}{P^{2}} - \frac{1}{Q^{2}}

sin (2 α - β - γ) + 8 sin (2 β - γ - α) + 27 sin (2 γ - α - β) = P

sin (α + β) + sin (β + γ) + sin (γ + α) = Q

then P+Q is equal to

p

q

are distinct reals , then

2 {(x - p) (x - q) + (p - x) (p - q) + (q - x) (q - p)} = {(p - q)}^{2} + {(x - p)}^{2}

+ {(x - q)}^{2}

is satisfied by

p = q + 2

p + q = 5

p^{2} - q^{2}

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