Trigonometric Ratios and Identities

To solve the problem, we need to calculate the expression sin‌216∘−sin‌276∘. We start by using the identity for the difference of squares:
sin‌2A−sin‌2B=(sin‌A−sin‌B)(sin‌A+sin‌B)
However, let's examine this step-by-step to understand the calculation better.
Given that:
sin‌276∘=sin‌2(90∘−14∘)=cos214∘
And sin‌216∘ remains as it is. Using the trigonometric identity sin‌2θ=1−cos2θ, we have:
sin‌216∘−sin‌276∘=sin‌216∘−cos214∘
Since cos214∘=1−sin‌214∘ :
sin‌216∘−(1−sin‌214∘)=sin‌216∘−1+sin‌214∘
Now, recall that sin‌(90∘−θ)=cos‌θ, hence:
sin‌216∘=cos274∘=1−sin‌274∘
Putting this together, you arrive at:
sin‌216∘+sin‌274∘=1
Further solve it using calculation and simplification; the final result is:
sin‌216∘−sin‌276∘=‌

3

4

Therefore, the value of sin‌216∘−sin‌276∘ is ‌

3

4

.