- If sec 0
13
5 , prove that
-
2 sin - 3 cos O
4 sin 0-9 cos O
= 3
Answers
Answer:
10 Cooling and Amazing Facts of Mathematics:
1. Zero ( 0 ) is the only number which can not be represented by Roman numerals.
2. What comes after a million, billion and trillion? A quadrillion, quintillion, sextillion, septillion, octillion, nonillion, decillion and undecillion
3. Plus (+) and Minus (-) sign symbols were used as early as 1489 A.D
4. 2 and 5 are the only primes that end in 2 or 5
5. An icosagon is a shape with 20 sides
6. Among all shapes with the same perimeter a circle has the largest area.
7. Among all shapes with the same area circle has the shortest perimeter
8. 40 when written "forty" is the only number with letters in alphabetical order, while "one" is the only one with letters in reverse order
9. 'FOUR' is the only number in the English language that is spelt with the same number of letters as the number itself
secθ=
B
H
=
5
13
Using Pythagoras Theorem,
H
2
=P
2
+B
2
13
2
=P
2
+5
2
P
2
=144
P=12
Now,
4sinθ−9cosθ
2sinθ−3cosθ
=
4(
13
12
)−9(
13
5
)
2(
13
12
)−3(
13
5
)
=
13
48−45
13
24−15
= 3