Question

If tan + sec 0 = 3, where is acute then prove that 5sin = 4​

Answer 1

Answer:

tanθ+secθ=4⇒cosθ1+sinθ=4⇒41+sinθ=cosθ

Also, we know that,

cos2θ=1−sin2θ⇒(41+sinθ)2=1−sin2θ⇒1+sin2θ+2sinθ=16−16sin2θ⇒17sin2θ+2sinθ−15=0⇒(sinθ+1)(17sinθ−15)=0⇒sinθ=1715 or −1

Therefore, Answer is 1715