Question

If 41sinA=40 show that tanA/tan^2A-1=360/1519

Answer 1

Answer:

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this very difficult

Answer 2

Answer:

Given that,

41 sinA = 40

Therefore, sinA = 40/41

sinA = opposite/hypotenuse = 40/41

So, opposite = 40 units

hypotenuse = 41 units

adjacent = √(hypotenuse² - opposite ²)

= √(41²) - (40)²

= √(1681 - 1600)

= √81 = 9

cosA = adjacent/hypotenuse = 9/41

tanA = sinA / cosA = (40/41) ÷ (9/41)

= 40/41 × 41/9 = 40/9

Now, let us take the LHS of the equation,

tanA / tan²A - 1

(40/9) ÷ (40/9)² - 1

40/9 ÷ (1600/81 - 1)

⇒ 40/9 ÷ ( 1600 - 81)/81

⇒ 40/9 ÷ 1519/81

⇒ 40/9 × 81/1519

⇒ 40 × 9/1519

⇒ 360/1519

Hence Proved