Test Index

ICSE Class X Math 2014 Solved Paper

© examsnet.com
Question : 51
Total: 52
Prove the identity:
(sin‌θ+cos‌θ)(tan‌θ+cot‌θ) = secθ+cosec‌θ
Solution:  
‌ L.H.S. ‌‌=(sin‌θ+cos‌θ)(tan‌θ+cot‌θ)
‌=(sin‌θ+cos‌θ)(‌
sin‌θ
cos‌θ
+‌
cos‌θ
sin‌θ
)
‌=(sin‌θ+cos‌θ)(‌
sin‌2θ+cos2θ
cos‌θ‌s‌i‌n‌θ
)
‌=(sin‌θ+cos‌θ)×‌
1
cos‌θ‌s‌i‌n‌θ
‌=‌
sin‌θ
cos‌θ‌s‌i‌n‌θ
+‌
cos‌θ
cos‌θ‌s‌i‌n‌θ
‌=‌
1
cos‌θ
+‌
1
sin‌θ
= secθ+cosec‌θ
‌=‌ R.H.S. ‌
© examsnet.com
Go to Question:
Prev Question
Next Question