# Evaluate the Following (Tan^2 60^@ + 4 Cos^2 45^@ + 3 Sec^2 30^@ + 5 Cos^2 90)/(Cosec 30^@ + Sec 60^@ - Cot^2 30^@) - Mathematics

#### Question

Evaluate the Following

(tan^2 60^@ + 4 cos^2 45^@ + 3 sec^2 30^@ + 5 cos^2 90)/(cosec 30^@ + sec 60^@ - cot^2 30^@)

#### Solution

(tan^2 60^@ + 4 cos^2 45^@ + 3 sec^2 30^@ + 5 cos^2 90)/(cosec 30^@ + sec 60^@ - cot^2 30^@)   ....(i)

By trigonometric ratios we have

tan 60^@ = sqrt3     cos 45^@ = 1/sqrt2    sec 30^@ = 2/sqrt3

cos 90^@ = 0      cosec  30^@ = 2      sec 60^@ = 2    cot 30^@ = sqrt3

By substituting above values in (i), we get

((sqrt3)^2 + 4.(1/sqrt3)^2 + 2 + [2/sqrt3]^2 + 5(0)^2)/(2 + 2sqrt2 (+ sqrt3)^2)

= (3 + 4. 1/2 + 3 4/3)/(4 - 3) = (3 + 2 + 4)/1 = 9

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#### APPEARS IN

RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 10: Trigonometric Ratios
Exercise 10.2 | 17 | Page no. 42
RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 10: Trigonometric Ratios
Exercise 10.2 | 17 | Page no. 42