Question

If tan theta = 12/5 then find value of sin square theta +cos square theta

Answer 1

Answer:

1

Step-by-step explanation:

Straight forward:

Irrespective of the value of Tanθ,  Sin²θ + Cos²θ is always equal to 1. (Trigonometric  identity Sin²θ + Cos²θ = 1)

Method 2:

But if you want to go and find value using the value of Tanθ, then you can do it as below:

Consider a right angled triangle with angle θ.

Tanθ = 12/5 = Opposite side to θ/Adjacent side to θ.

Using Pythagoras theorem we know that

Adjacent side² + Height ² = Hypotenuse²

12² + 5² = hypotenuse²

=> Hypotenuse = √169 = 13.

Now Sinθ = Opposite side to θ/Hypotenuse = 12/13

       Cosθ = Adjacent side to θ/Hypotenuse = 5/13.

Sin²θ + Cos²θ = (12/13)² + (5/13)² = 144 + 25/169 = 169/169 = 1.

Answer 2

Step-by-step explanation:

cos=5/13,cot=5/12,cos=5/13,cosec=13/12. answer = 209/229