Question

cos^2 30 cos^2 45 + 4 sec^2 60 + 1/2 cos^2 90 - 2 tan^2 60 = ? (a) 73/8 (b) 75/8 (c) 81/8 (d) 83/8

Answer 1

Answer:      Option (a)  83/8

Step-by-step explanation:

we know

cos 30 is = √3/2

and cos 45 = 1/√2

sec 60 = 2

tan 60= √3

then we can write

cos^2 30 cos^2 45 + 4 sec^2 60 + 1/2 cos^2 90 - 2 tan^2 60  is now

= (√3/2) ^2 X (1/√2)^2 + 4 X (2)^2 + 1/2 X 0 - 2 X (√3)^2  

= 3/4 X 1/2 + 16 + 0 - 6

= 3/8 + 10

= (3+80)/8

= 83/8

Answer 2

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