Question

The value of 0 (0 degrees < theta < 90 degrees) * i * f (a) 30 degrees 2cos^2 theta = 1/2 (b) 60 degrees (c) 45 degrees (d) 90°​

Answer 1

Step-by-step explanation:

) 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