if sin theta + cos theta = √2[sin(90-theta)] , then find the value of tan theta
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Answered by
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} \sin(90 - x)](https://tex.z-dn.net/?f=+%3D++%26gt%3B++%5C%3A++%5Csin%28x%29++%2B++%5Ccos%28x%29++%3D++%5Csqrt%7B2%7D+%5Csin%2890+-+x%29+)
![= > \: \sin(x) + \cos(x) = \sqrt{2} \cos(x) = > \: \sin(x) + \cos(x) = \sqrt{2} \cos(x)](https://tex.z-dn.net/?f=+%3D++%26gt%3B++%5C%3A++%5Csin%28x%29++%2B++%5Ccos%28x%29++%3D++%5Csqrt%7B2%7D+%5Ccos%28x%29+)
![= > \: \sin(x) = \sqrt{2} \cos(x) - \cos(x) = > \: \sin(x) = \sqrt{2} \cos(x) - \cos(x)](https://tex.z-dn.net/?f=+%3D++%26gt%3B++%5C%3A++%5Csin%28x%29++%3D++%5Csqrt%7B2%7D++%5Ccos%28x%29++-++%5Ccos%28x%29+)
![= > \: \sin(x) = ( \sqrt{2} - 1) \cos(x) = > \: \sin(x) = ( \sqrt{2} - 1) \cos(x)](https://tex.z-dn.net/?f=+%3D++%26gt%3B++%5C%3A++%5Csin%28x%29++%3D+%28+%5Csqrt%7B2%7D++-+1%29+%5Ccos%28x%29+)
![= > \: \frac{ \sin(x) }{ \cos(x) } = \sqrt{2} - 1 = > \: \frac{ \sin(x) }{ \cos(x) } = \sqrt{2} - 1](https://tex.z-dn.net/?f=+%3D++%26gt%3B++%5C%3A++%5Cfrac%7B+%5Csin%28x%29+%7D%7B+%5Ccos%28x%29+%7D++%3D++%5Csqrt%7B2%7D++-+1)
![= > \: \tan(x) = \sqrt{2} - 1 = > \: \tan(x) = \sqrt{2} - 1](https://tex.z-dn.net/?f=+%3D++%26gt%3B++%5C%3A++%5Ctan%28x%29++%3D++%5Csqrt%7B2%7D++-+1)
:-)Hope it helps u.
the answer is here,
I take theta as x.
:-)Hope it helps u.
Answered by
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...... :-)
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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