Question

prove that: cot (A+B)=cot A cot B-1/cot A+cot B

note: prove using LHS

Answer 1

Step-by-step explanation:

LHS:

cot (A+B)

cos(A+B)÷sin(A+B)

According to the formula,

cos(A+B) can be written as cosA cosB -sin A sin B.

similarly,

sin(A+B) can be written as sinA cosB +cosA sin B

substitute these formula in cos(A+B)÷sin (A+B)

And divide both the numerator and denominator by

sinA sin B

That is ,

cos A÷sinA×cos B÷ sin B -sin A sin B ÷sin A sin B whole divided by sin A cos B ÷ sin A sin B + cos A sin B ÷ sin A sin B

you will get;

cot A cot B - 1 ÷ cot B + cot A

LHS=RHS

hence proved .

Answer 2

Answer:

HS:

cot (A+B)

cos(A+B)÷sin(A+B)

According to the formula,

cos(A+B) can be written as cosA cosB -sin A sin B.

similarly,

sin(A+B) can be written as sinA cosB +cosA sin B

substitute these formula in cos(A+B)÷sin (A+B)

And divide both the numerator and denominator by

sinA sin B

That is ,

cos A÷sinA×cos B÷ sin B -sin A sin B ÷sin A sin B whole divided by sin A cos B ÷ sin A sin B + cos A sin B ÷ sin A sin B

you will get;

cot A cot B - 1 ÷ cot B + cot A

LHS=RHS

Step-by-step explanation:

sorry upar se liye cause i am in class 7

and yeh class 10th ka hai na ?