Question

solve this plzzzz..........​

Answer 1

$\boxed{\begin{minipage}{7 cm}Fundamental Trigonometric Identities \\ \\ \sin^2\theta + \cos^2\theta=1 \\ \\1+\tan^2\theta = \sec^2\theta \\ \\1+\cot^2\theta = \text{cosec}^2 \, \theta \end{minipage}}$

$\mathfrak{Question:-}$

show that sinA.cosB - cosA.sinB = sin(a-b), where a = 60 and b = 30

$\mathfrak{Answer:-}$

$\mathsf{Given:-}$

A = 60

B = 30

So,

$\bold{SinA.CosB - CosA.SinB = Sin(A-B)}$

$\bold{Sin\;60 \times Cos\; 30 - Cos\; 60 \times Sin\; 30 = Sin (A-B)}$

$\bold{=\frac{\sqrt{3}}{2} \times \frac{\sqrt{3}}{2} - \frac{1}{2} \times \frac{1}{2} = Sin(60 - 30)}$

$\bold{=(\frac{\sqrt{3} }{2})^{2} - (\frac{1}{2})^{2} = Sin\;30}$

$\bold{=\frac{3}{4} - \frac{1}{4} = \frac{1}{2}}$

$\bold{\frac{1}{2}=\frac{1}{2}}$

$\bold{LHS = RHS}$

Hence it is verified.