Question

if sino =12/13 and o is less than 90° find the value of (cos o+tan o)​

Answer 1

Answer:

If sinθ =12/13 and θ is less than 90°, the value of (cos θ+tan θ)​ is $\frac{181}{65}$.

Step-by-step explanation:

It is given that sinθ =12/13.

sin θ = $\frac{opposite side}{hypotenuse}$

Hence we can calculate the value of the adjacent side to the angle θ by the following method:

Let the lengths of opposite side and hypotenuse be 12x and 13x respectively.

Then using Pythagoras theorem,

(Adjacent side)² = (hypotenuse)² - (opposite side)²

                          = (13x)² - (12x)²

                          = 169x² - 144x²

                          = 25x²

∴ Adjacent side = √25x² = 5x

Now, cosθ = $\frac{adjacent side}{hypotenuse}$

                  = $\frac{5x}{13x}$

                  = $\frac{5}{13}$.

Similarly tanθ = $\frac{opposite side}{adjacent side}$

                        = $\frac{12x}{5x}$

                        = $\frac{12}{5}$.

Now we can calculate the value of cos θ + tan θ:

cosθ + tanθ = $\frac{5}{13}+ \frac{12}{5}$

Taking LCM

cosθ + tanθ = $\frac{5\times5+12\times13}{13\times5}$

                    = $\frac{25+156}{65}$

                    = $\frac{181}{65}$.

Hence the value of cosθ + tanθ when sinθ =12/13 and θ is less than 90° is 181/65.