Question

If tanA+cotA=2,find sinA

Answer 1

Hii !!!

tanA + cotA = 2

sinA / cosA + cosA / sinA = 2

sin²A + cos²x / sinA × cosA = 2

1 /sinAcosA = 2

1 = 2sinA cosA

•°• 2sinA cosA = sin2A

hence, sin2A= 1

sin2A = sin90°

2A = 90°

A = 45°

hence, sinA = sin45° = 1/√2

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Hope it helps you !!!

@Rajukumar111

Answer 2

Bonjour!

Given=> tanA + cotA = 2

$\frac{1}{cos \: a \times sin \: a} = 2$

$= > tan \: a + \frac{1}{tan \: a} = 2$

$= > \frac{ {tan}^{2}a + 1 }{tan \: a} = 2$

$= > \frac{ {sec \: }^{2} a}{tan \: a} = 2$

$= > \frac{ \frac{1}{ {cos \: }^{2}a } }{tan \: a} = 2$

$= > \frac{1}{ {cos}^{2} a \times \frac{sin \:a }{cos \: a} } = 2$

$= > \frac{1}{sin \: a \times cos \: a} = 2 \\ \\ = > \frac{1}{cos \: a} = 2sin \: a \\ \\ = > 2sin \: a = sec \: a \\ \\ = > sin \: a = sec \: a \div 2$

As, we know tan45° and cot45° is equal to 1.

So, sin45° = 1/√2

OR

sin45° = sec45°/2

= √2/2

= 1/√2

Hope this helps...:)