Question

Given sec(theta)= 5... find cot(90-theta)

Answer 1

`\sec(\theta)=(1)/(\cos(\theta)) \\ \\\cos(\theta)=(1)/(\sec(\theta))=(1)/(5) \\ \\ \sin^2\theta+\cos^2\theta=1 \\ \\\sin\theta= √(1-\cos^2\theta)= \sqrt{1-( (1)/(5))^2 } = \sqrt{1- (1)/(25) } = \sqrt{ (25)/(25) -(1)/(25) }=\frac { √(24)}{5} \\ \\ \cot(90^o-\theta)=tan(\theta)= (\sin\theta)/(\cos\theta) = \frac{\frac { √(24)}{5} }{ (1)/(5) } = √(24) = √(4*6)=2 √(6) \\`