Question

$if \: \: \sin o + \cos o = \sqrt{3} \: \\ then \: prove \: that \: \tan o + \cot o = 1$
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Answer 1

Step-by-step explanation:

Given :-

Sin o + Cos o = √3

On squaring both sides then

=>(Sin o + Cos o)^2 =( √3 )^2

It is in the form of (a+b)^2

Where,a=Sin o and b=Cos o

we know that (a+b)^2 = a^2 +2ab+b^2

=>Sin^2 o +2 Sin o Cos o + Cos^2 o = 3

We know that

Sin^2 o + Cos^2 o = 1

=>1+2 Sin o Cos o = 3

=> 2 sin o Cos o = 3-1

=>2 Sin o Cos o = 2

=>Sin o Cos o = 2/2

=>Sin o Cos o = 1

Therefore,Sin o Cos o = 1 -----(1)

Now LHS = Tan o + Cot o

we know that

Tan A = Sin A/ Cos A

Cot A = Cos A/ Sin A

=>(Sin o/Cos o) +(Cos o/Sin o)

=>[(Sin0×Sin o)+(Cos o ×Cos o)]/Sin o Cos o

=>(Sin^2 o + Cos^2 o)/(Sin o Cos o)

We know that

Sin^2 o + Cos^2 o = 1

=>1/ Sin o Cos o

From (1)

=>1/1

=>1

=>RHS

LHS=RHS

Answer:-

If Sin o + Cos o = √3 then Tan o + Cot o = 1

Used formulae:-

• Sin^2 A + Cos^2 A= 1
• Tan A = Sin A/ Cos A
• Cot A = Cos A/ Sin A