If 41sinA=40 show that tana/tan^2-1=360/1519
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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✓
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Step-by-step explanation:
41sinA=40 show that tana/tan^2-1=360/1519
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