Question

If tan A = 3/4, then show that sin A. cos A = 12/25.

Sahi Solution hona chahiye bss kahi se chep ke do​

Answer 1

Answer:

$here \: is \: your \: answer \: dear$

Answer 2

S O L U T I O N :

$\underline{\bf{Given\::}}$

tan A = 3/4

$\underline{\bf{Explanation\::}}$

Firstly, attachment a figure of right angled Δ according to the given question.

As we know that,

$\boxed{\bf{tan\:\theta = \frac{Perpendicular}{Base} }}$

A/q

$\mapsto\tt{tan\:A = \dfrac{3}{4} = \dfrac{AC}{AB} }$

$\underline{\underline{\tt{Using\:\:by\:\:Pythagoras\:\:theorem\::}}}$

$\mapsto\sf{(Hypotenuse)^{2} = (Base)^{2} + (Perpendicular)^{2}}$

$\mapsto\sf{(BC)^{2} = (AB)^{2} + (AC)^{2}}$

$\mapsto\sf{(BC)^{2} = (4)^{2} + (3)^{2}}$

$\mapsto\sf{(BC)^{2} = 16 + 9}$

$\mapsto\sf{(BC)^{2} =25}$

$\mapsto\sf{BC =\sqrt{25} }$

$\mapsto\bf{BC =5\:unit}$

Now,

Taking L.H.S :

$\mapsto\tt{sin\:A \times cos \:A}$

$\mapsto\tt{\dfrac{Perpendicular}{Hypotenuse} \times \dfrac{Base}{Hypotenuse} }$

$\mapsto\tt{\dfrac{AC}{BC} \times \dfrac{AB}{BC} }$

$\mapsto\tt{\dfrac{3}{5} \times \dfrac{4}{5} }$

$\mapsto\bf{\dfrac{12}{25} }$

Thus,

L.H.S = R.H.S