Question

for traingle , PQR prove that tan[Q+R/2]=cotP/2​

Answer 1

Step-by-step explanation:

Angle P + Angle Q + Angle R = 180°

… ( Angle sum property of triangle )

Consider above equation as 1

Divide equation 1 by 2 , we get

P/2 + Q/2 + R/2 = 90°

P/2 + Q/2 = 90° - R/2

Taking tan to both the side,

tan ( P+Q/2) = tan (90°- R/2)

tan ( P+Q/2) = cot R/2

Since tan(90°-0) = cot0

Hence proved.

Answer 2

Answer: So as per angle sum property (ANGLE P +ANGLE Q+ANGLE R=180)

So dividing both sides by 2 we get:-

(P+Q+R)/2=90

Now taking p/2on LHSwe get:-Q+R/2=90-p/2

Now if we give tan both the sides then:-

Tan(Q+R/2)=Tan(90-p/2)

And as tan(90-A)is cotA so hence Tan(Q+R/2)=cotp/2

I hope this helps..