# Find The Numerical Value ? If

Answered

The numerical value of

cos^{2}45^{o}/sin^{2}60^{o} + cos^{2}60^{o}/sin^{2}45^{o} – tan^{2}30^{o}/cot^{2}45^{o} – Sin^{2}30^{o}/cot^{2}30^{o}

- 5/4
- 1/4
- 3/4
- 1/2

Best answer

**Answer: (3) 3/ 4**

**Explanation:-**

cos^{2}45^{o}/sin^{2}60^{o} + cos^{2}60^{o}/sin^{2}45^{o} – tan^{2}30^{o}/cot^{2}45^{o} – Sin^{2}30^{o}/cot^{2}30^{o}

= (1/sqrt.2)^{2} / (sqrt.3/2)^{2} + (1/2)^{2}/ (1/sqrt.2)^{2} – (1/sqrt.3)^{2} /(1)^{2} – (1/2)^{2}/(sqrt.3)^{2}

= (1/2)/(3/4) + (1/4)/(1/2) – (1/3)/1 – (1/4)/(3)

= 1 x 4/2 x 3 + 1 x 2/1 x 4 – 1 x 1/3 – 1/ 4 x 3

= 2/3 + 1/ 2 – 1/ 3 – 1/ 12

= (2 x 4 + 1 x 6 – 1 x 4 – 1 x 1)/12

= (8 + 6 – 4 – 1)/12

= (14 – 5)/12

= 9 / 12

= 3 / 4

Hence, the answer is (3) 3 / 4.