find angle theta in the following if 0°<thetha <90° 1) tan theta / 2 = cot 2 thetha
Answers
Answered by
1
Solution
A) 2cos
2
θ+sinθ−2=0
or, 2−2sin
2
θ+sinθ−2−0
or, sinθ(−2sinθ+1)=0
Since θ
=0, sinθ=
2
1
⇒θ=30
o
. [Since 0
o
<θ<90
o
]
B) 3cosθ=2sin
2
θ
or, 3cosθ=2−2cos
2
θ
or, 2cos
2
θ−3cosθ−2=0
or, (2cosθ−1)(cosθ+2)=0
Since cosθ
=−2, cosθ=
2
1
⇒θ=60
o
[Since 0
o
<θ<90
o
]
C) sec
2
θ−2tanθ=0
or, 1+tan
2
θ−2tanθ=0
or, (tanθ−1)
2
=0
⇒tanθ=1⇒θ=45
o
[Since 0
o
<θ<90
o
]
D) tan
2
θ=3(secθ−1)
or, sec
2
θ−1=3(secθ−1)
or, sec
2
θ−3secθ+2=0
or, (secθ−1)(secθ−2)=0
Since 0
o
<θ<90
o
, secθ=2⇒θ=60
0
.
Similar questions