Q. If 7sinθ+24cosθ=25, then what is the value is sinθ+cosθ

 Q. If 7sinθ+24cosθ=25, then what is the value is sinθ+cosθ

Ans.

Before read or write answer first read below points:

First differenriate both sides with respect to x. 

Then you will get equation and equals to 0.

Now you are able to take any value in right side of the equals right side. 

Then you will get tan theta value. 

From there you can find sin theta snd cos theta. 

Now 

ATQ, 

putting the value of sin and cos. 

Given,

7sinθ+24cosθ=25

differentiate with respect to x

dy/dx=d(7sinθ+24cosθ)/dx

         =d(7sinθ)/dx+d24cosθ/dx=0

        because derivative of  constant is 0.

     =7*cosθ-24*sinθ=0

     7cosθ=24sinθ

sinθ/cosθ=7/24

tanθ=7/24

P=7

B=24

By pythogoras theorem,

H^2=P^2+B^2

           =7*7+24*24

           =625

H=25

ATQ,

sinθ+cosθ=P/H+B/H

                =7/25+24/25=31/25

ans.Given 

7sintheta+24costheta=25