Question

If sin theta=12/13 then value of 2cos theta+3tan theta/sin theta+tan theta^sin theta

Answer 1

Trigonometry problem

Given: sinθ = 12/13

To find: (2 cosθ + 3 tanθ)/(sinθ + tanθ)

Solution:

• Here, sinθ = 12/13
• Then, cosθ = √(1 - sin²θ), since sin²A + cos²A = 1
• or, cosθ = √{1 - (12/13)²}
• or, cosθ = √(1 - 144/169)
• or, cosθ = √{(169 - 144)/169}
• or, cosθ = √(25/169)
• or, cosθ = 5/13

So, tanθ = sinθ/cosθ

or, tanθ = 12/5

∴ (2 cosθ + 3 tanθ)/(sinθ + tanθ)

= (2 * 5/13 + 3 * 12/5) / (12/13 + 12/5)

= (10/13 + 36/5) / (12/13 + 12/5)

= {(50 + 468)/65} / {(60 + 156)/65}

= 518/216

= 259/108

Answer: (2 cosθ + 3 tanθ)/(sinθ + tanθ) = 259/108 .