Math, asked by mohisharma, 1 year ago

if sin theta + cos theta = √2[sin(90-theta)] , then find the value of tan theta

Answers

Answered by jaya1012
3
hii. ......friend

the answer is here,

I take theta as x.

 =  >  \:  \sin(x)  +  \cos(x)  =  \sqrt{2} \sin(90 - x)

 =  >  \:  \sin(x)  +  \cos(x)  =  \sqrt{2} \cos(x)

 =  >  \:  \sin(x)  =  \sqrt{2}  \cos(x)  -  \cos(x)

 =  >  \:  \sin(x)  = ( \sqrt{2}  - 1) \cos(x)

 =  >  \:  \frac{ \sin(x) }{ \cos(x) }  =  \sqrt{2}  - 1

 =  >  \:  \tan(x)  =  \sqrt{2}  - 1

:-)Hope it helps u.
Answered by Panzer786
2
Heya dear !!!


Sin theta + Cos theta = ✓2 Sin (90- Theta)






Sin theta + Cos theta = ✓2 Cos theta [ Sin (90-theta = Cos theta]




Sin theta = ✓2 Cos theta - Cos theta




Sin theta = Cos theta ( ✓2 - 1)





Sin theta/ Cos theta = ✓2-1 ----(1)



As we know that,


Tan theta = Sin theta/ Cos theta





Therefore,





From equation (1) we have,



Sin theta/Cos theta = ✓2-1





Tan theta = ✓2-1




:-) ......... HOPE IT WILL HELP YOU...... :-)

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