What is the value of \(\frac{5\,sin\,75°\,sin\,77°+2\,cos\,13°cos\,

1.	What is the value of \(\frac{5\,sin\,75°\,sin\,77°+2\,cos\,13°cos\,15°}{cos\,15°sin77°}\) - \(\frac{7\,sin\,81°}{cos\,90}\)?(a) –1 (b) 0(c) 1 (d) 2
Answer» \(\frac{5\,sin\,75°\,sin\,77°+2\,cos\,13°cos\,15°}{cos\,15°sin77°}\) - \(\frac{7\,sin\,81°}{cos\,90}\) = \(\frac{5\,sin\,(90°-15°)\,sin\,77°+2\,cos\,(90°-77°)cos\,15°}{cos\,15°sin\,77°}\) - \(\frac{7\,sin\,(90°-9°)}{cos\,9°}\) = \(\frac{5\,cos\,15°\,sin\,77°+2\,sin\,77°cos\,15°}{cos\,15°sin\,77°}\) - \(\frac{7\,sin\,9°}{cos\,9°}\) = \(\frac{5\,cos\,15°\,sin\,77°}{cos\,15°sin\,77°}\) - \(\frac{7\,sin\,9°}{cos\,9°}\) = 7 - 7 = 0.

What is the value of \(\frac{5\,sin\,75°\,sin\,77°+2\,cos\,13°cos\,15°}{cos\,15°sin77°}\) - \(\frac{7\,sin\,81°}{cos\,90}\)?(a) –1 (b) 0(c) 1 (d) 2

Answer»

\(\frac{5\,sin\,75°\,sin\,77°+2\,cos\,13°cos\,15°}{cos\,15°sin77°}\) - \(\frac{7\,sin\,81°}{cos\,90}\)

= \(\frac{5\,sin\,(90°-15°)\,sin\,77°+2\,cos\,(90°-77°)cos\,15°}{cos\,15°sin\,77°}\) - \(\frac{7\,sin\,(90°-9°)}{cos\,9°}\)

= \(\frac{5\,cos\,15°\,sin\,77°+2\,sin\,77°cos\,15°}{cos\,15°sin\,77°}\) - \(\frac{7\,sin\,9°}{cos\,9°}\)

= \(\frac{5\,cos\,15°\,sin\,77°}{cos\,15°sin\,77°}\) - \(\frac{7\,sin\,9°}{cos\,9°}\) = 7 - 7 = 0.