Question

If π/2 π and sin A = 4/5 , then tan A/2 =??

Answer 1

Answer: 2

Explanation:

`\text{If the angle is in Quadrant II and sin A }=(4)/(5), \text{then cos A }=-(3)/(5).\\use\ Pythagorean\ Theorem: x^2+4^2=5^2\implies x=3,\quad cos =(x)/(h)\\\\\\tan\bigg((A)/(2)\bigg)=(1-cosA)/(sinA)\\\\\\.\qquad \qquad =(1-(-(3)/(5)))/((4)/(5))\\\\\\.\qquad \qquad =((8)/(5))/((4)/(5))\implies (8)/(5)/(4)/(5)\implies (8)/(5)*(5)/(4)=(8)/(4)=\large\boxed{2}`