Question

if tanA = 3÷4 show that sinAcosA = 12÷25

Answer 1

Heya !!!




TanA = 3/4 = P/B




P = 3. and B = 4




By pathagarous theorem , we have



(H)² = (B)² + (P)²




(H)² = (4)² + (3)²






H = root 25



H = 5



Therefore,



SinA = P/H = 3/5




And,



CosA = B/H = 4/5







---------------------------------------------





SinA × Cos A = 12/25






LHS = SinA × CosA




=> 3/5 × 4/5





=> 12/25




Hence,



LHS = RHS.....PROVED.....







★ ★ ★ HOPE IT WILL HELP YOU ★ ★ ★

Answer 2

$\bf \: Hello \:there$

• Given :-

$\tan( \theta) = \frac{3}{4} \\ \\ we \: know \: \\ \\ \boxed{ tan\theta = \frac{p}b }$
By Pythagoras theorem -

H² = P²+B²

H = √(3²+4²) = 5

Now according to the question -
$sin \theta.cos \theta = \frac{12}{25} \\ \\ \Rightarrow \frac{3}{5} \times \frac{4}{5} = \frac{12}{25} \\ \\ \Rightarrow \frac{12}{25} = \frac{12}{25}$

Hope this helps you ☺