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# Without using trigonometric tables, evaluate the following (6 to 10): 6. (i) cos2 26o + cos 64o sin 26o + (tan 36o/ cot 54o) (ii) (sec 17o/ cosec 73o) + (tan 68o/ cot 22o) + cos2 44o + cos2 46o

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This question is from the Book- ML Aggarwal
Board- ICSE
Publication- Avichal
Chapter- Trigonometric Identities
Chapter number-18
This ques has been asked in 2012 exam. So it is very important ques for this point of view.

Without using trigonometric tables, evaluate the following (6 to 10):

6. (i) cos2 26o + cos 64o sin 26o + (tan 36o/ cot 54o)

(ii) (sec 17o/ cosec 73o) + (tan 68o/ cot 22o) + cos2 44o + cos2 46o

Class10th ML Aggarwal, ICSE board

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1. Solution:

Given,

(i) cos2 26o + cos 64o sin 26o + (tan 36o/ cot 54o)

= cos2 26o + cos (90o – 16o) sin 26o + [tan 36o/ cot (90o – 54o)]

= [cos2 26o + sin2 26o] + (tan 36o/ tan 36o)

= 1 + 1 = 2

(ii) (sec 17o/ cosec 73o) + (tan 68o/ cot 22o) + cos2 44o + cos2 46o

= [sec 17o/ cosec (90o – 73o)] + [(tan 90– 22o)/ cot 22o] + cos2 (90o – 44o) + cos2 46o

= [sec 17o/ sec 17o] + [cot 22o/ cot 22o] + [sin2 46o + cos2 46o]

= 1 + 1 + 1

= 3

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