Question

if tan theta+sec theata=4 FIND sin theta +cos theta​

Answer 1

Answer:

23/17

Explanation:

Here,

tan(theta) +sec(theta)=4 ..........1

now as,

1+{tan}^{2}( theta) ={sec}^{2}(theta)

or {sec}^{2}(theta)-{tan}^{2}(theta)=1

or [sec(theta)+tan(theta)][sec(theta)-tan(theta)]=1

Now from eq. 1 and above eq. ,we get

4[sec(theta)-tan(theta)]=1

or sec(theta)-tan(theta) =1/4 ........ 2

On adding eq. 1 and eq. 2 we get

2sec(theta) =4+1/4

or 2sec(theta) =(16+1)/4

or sec(theta) =17/8

or cos(theta) =8/17 ........3

now, from eq. 1

sin(theta) /cos(theta) + 1/cos(theta) =4

or [sin(theta) +1]/cos(theta) =4

or sin(theta) +1=4cos(theta)

or sin(theta) =4cos(theta) -1

from eq. 3 and above eq. we have

sin(theta) =4(8/17) -1

or sin(theta) =32/17-1

or sin(theta) =(32-17)/17=15/17 ........4

adding eq. 3 and eq. 4 we get,

sin(theta) +cos(theta) =8/17+15/17

=23/17 is required answer