Question

What is the value of (cos 18° - sin 18°)/sin 27°​

Answer 1

Answer:

The value of $\dfrac{cos18^o-sin18^o}{sin27^o}$ is 1.417      

Step-by-step explanation:

We have to find the value of $\dfrac{cos18^o-sin18^o}{sin27^o}$ -----(i)

where,

• $cos18^o$ = 0.951
• $sin18^o$ = 0.309
• $sin27^o$ = 0.453

Now,

put the above values in equation (i)

$\dfrac{cos18^o-sin18^o}{sin27^o}$

= $\dfrac{0.951-0.309}{0.453}$

= $\dfrac{0.642}{0.453}$

= 1.417                                                                

Answer 2

Answer:

Step-by-step explanation:

Ans:

The value of (cos18-sin18)/sin27= $\sqrt{2}$ =1.414

First let's find the value of cos18-sin18 ⇒

cos8-sin18 = sin72-sin18

= 2cos((72+18)/2)sin((72-18)/2)    

∵ sinA - sinB = 2sin((A-B)/2)cos((A+B)/2)

= 2cos(90/2)sin(54/2)

⇒cos18-sin18=2cos45sin27

Bringing 'sin27' to the LHS ⇒

(cos18-sin18)/sin27=2 × $\frac{1}{\sqrt{2} }$ = $\sqrt{2}$ ≅ 1.414