Question

if sin thetha = c/under root c²+d²and d>0,find the value of cos theta and tan theta
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Answer 1

Step-by-step explanation:

$sin \theta = \frac{c}{\sqrt{(c^2+d^2)} } \\\\ sin\theta=\frac{opposte \ side \ of \ angle \ \theta}{hypotenuse} \\\\ we \ know, hypotenuse^2=(opp. \ side)^2+(adj. \ side)^2 \\ {\sqrt{(c^2+d^2)}^2 = c^2+(adj. \ side)^2$

$c^2+d^2=c^2+(adj. \ side)^2 \\ adjacent \ side =d \\\\ =>cos\theta =\frac{adjacent \ side \ of \ angle \ \theta}{hypotenuse} =\frac{d}{\sqrt{(c^2+d^2)}} \\\\=> tan \theta=\frac{opposite \ side \ of angle \ \theta}{adjacent \ side \ of angle \ \theta} = \frac{c}{d}$