This ques has been asked in 2010. So it is very important ques.
This ques has been taken from the Book ML Aggarwal
Board- ICSE
Publication- Avichal
Chapter- Trigonometric Identities
Chapter number-18
Without using trigonometric tables, evaluate the following (i) (sin 35o cos 55o + cos 35o sin 55 o)/ (cosec2 10o – tan2 80 o) (ii) sin2 34o + sin2 56o + 2 tan18o tan 72o – cot2 30o
Question no. 8, class10, 18th chapter
Given,
(i) (sin 35o cos 55o + cos 35o sin 55 o)/ (cosec2 10o – tan2 80 o)
(ii) sin2 34o + sin2 56o + 2 tan18o tan 72o – cot2 30o
= sin2 34o + sin2 (90o – 34o) + 2 tan18o tan (90o – 18o) – cot2 30o
= [sin2 34o + cos2 34o] + 2 tan18o cot 18o – cot2 30o
= 1 + 2 x 1 – (√3)2
= 1 + 2 – 3
= 0