Question

find the value of the following without using trigonometric tables cos50/2sin40+4(cosec^2 59°-tan^2 31°)/3tan^2 45°-2/3tan12×tan78×sin90

Answer 1

1/2+4/3-2/3*1
1/2+4/3-2/3
1/2+2/3
7/6

Answer 2

Answer:

7/6

Steps:

cos50 = sin (90-50) = sin40

Cos50/2sin40 = sin40/2sin40 = 1/2 --------------------------- i

tan²31 = cot²(90-31) = cot²31

tan45 = 1

4(cosec²31 - cot²31)/3tan45

4(1)/3     [cosec²θ - cot²θ = 1] -------------- ii

tan12 = cot(90-12) = cot78

sin90 = 1

2/3 (1)(1)

2/3 ---------------------------- iii

Applyng functions in i, ii, iii:

1/2 + 4/3 -2/3 = 7/6

Thank you