Question:
What is (p + q) equal to?
What is (p + q) equal to?
Options:
- a) sec 4a
- b) cosec 4a
- c) 2sec 4a
- d) 2cosec 4a
- a) sec 4a
- b) cosec 4a
- c) 2sec 4a
- d) 2cosec 4a
correct answer : d)
Explanation:
p + q = tan 2 a – tan a + cot a
– cot 2a
=
sinc os
sin ·co s
co ss in
sin ·co s
22 2222
22
αα
αα
αα
αα
-
+ -
= sinc os
sin ·co s
co ss in
sin ·co s
22 2222
22
αα
αα
αα
αα
– + –
= – +24
4
22
2
cos
sin
cos
sin
α
α
α
α
= 24 24 2
42
(sin ·co sc os ·sin)
sin ·sin
αα αα
αα
–
= 24 2
42
sin( )
sin ·sin
αα
αα
–
= 22
42
.sin
sin ·sin
α
αα
= 2cosec 4a.
p + q = tan 2 a – tan a + cot a
– cot 2a
=
sinc os
sin ·co s
co ss in
sin ·co s
22 2222
22
αα
αα
αα
αα
-
+ -
= sinc os
sin ·co s
co ss in
sin ·co s
22 2222
22
αα
αα
αα
αα
– + –
= – +24
4
22
2
cos
sin
cos
sin
α
α
α
α
= 24 24 2
42
(sin ·co sc os ·sin)
sin ·sin
αα αα
αα
–
= 24 2
42
sin( )
sin ·sin
αα
αα
–
= 22
42
.sin
sin ·sin
α
αα
= 2cosec 4a.