UPSC NDA I 2015 Mathematics Solved Paper

Given: 25cos2θ+5‌cos‌θ−12=0 , where ‌

π

2

<α<π
To find: tan‌α
25cos2θ+5‌cos‌θ−12=0
⇒cos‌θ=‌

−5±√52−4(25)(−12)

2(25)

⇒cos‌θ=‌

−5±35

50

⇒cos‌θ=−4∕5‌ or ‌cos‌θ=3∕5
Now, ‌

π

2

<α<π . So, cos‌α is negative.
∴cos‌α=−4∕5
So, cos‌α=−4∕5 , where α is in second quadrant.
∴sin‌α should be positive.
sin‌α=√1−cos2α
⇒sin‌α=√1−‌

16

25

⇒sin‌α=3∕5
Now, tan‌α=‌

sin‌α

cos‌α

⇒tan‌α=−3∕4