Question

Sin 70°cos10°-cos70°sin10°=√3/2

Answer 1

Step-by-step explanation:

LHS

= Sin 70°cos10°-cos70°sin10°

= sin(70° - 10°)

= sin60°

=√3/2 = RHS (PROVED)

Answer 2

Answer:

Required answer is Sin 70°cos10°-cos70°sin10°=√3/2

Step-by-step explanation:

We have to proof that Sin 70°cos10°-cos70°sin10°=√3/2

Let left hand side =

$\sin( {70}^{o} ) \cos( {10}^{o} ) - \cos( {70}^{o} ) \sin( {10}^{o} )$

And right hand side =

$\frac{ \sqrt{3} }{2}$

Now from left hand side,

$\sin( {70}^{o} ) \cos( {10}^{o} ) - \cos( {70}^{o} ) \sin( {10}^{o} )$

$= \sin( {70}^{o} - {10 }^{o} ) = \sin( {60}^{o} ) = \frac{ \sqrt{3} }{2}$

Left hand side = Right hand side ( proof)

Here applied formula is

$\sin(a) \cos(b) - \sin(b) \cos(a) = \sin(a - b)$