Question

sin A cos A (tanA+cot A)=1​

Answer 1

Answer:

Step-by-step explanation:

We have,

$\tt{sin(A)\,cos(A)\{tan(A)+cot(A)\}}$

$\sf{=sin(A)\,cos(A)\bigg\{\dfrac{sin(A)}{cos(A)}+\dfrac{cos(A)}{sin(A)}\bigg\}}$

$\sf{=sin(A)\,cos(A)\bigg\{\dfrac{sin^2(A)+cos^2(A)}{cos(A)sin(A)}\bigg\}}$

$\sf{=sin(A)\,cos(A)\bigg\{\dfrac{1}{cos(A)sin(A)}\bigg\}}$

$\sf{=1}$