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(1+sinθ)/cosθ = x sinθ/cosθ + 1/cosθ = x tanθ + secθ = x ...........................(i) secθ = x – tanθ On squaring both sides, (secθ)2 = (x-tanθ)² sec²θ = x²+ tan²θ-2xtanθ sec²θ-tan²θ = x² -2xtanθ 1 = x² -2xtanθ tanθ = (x²-1)/2x Now putting the value of tanθ in equation (i) (x²-1)/2x + secθ = x secθ = x - (x²-1)/2x secθ = (2x²-x²+1)/2x = (x2+ 1)/2x Alternate method: (1+sinθ)/cosθ = x sinθ/cosθ + 1/cosθ = x tanθ + secθ = x secθ+tanθ = x ...........................(i) So secθ-tanθ = 1/x ...........................(ii) {As sec2θ - tan2 θ = 1 } Adding both equations 2secθ = x + 1/x = (x2+1)/x So secθ = (x2+1)/2x
630.11 ÷ 20.98 × 5.14 – 125.9 = √?
837.04 × 4.02 + 40.04% of 3049.98 – 3667.82 = ? 2 – 60.87
(2520.33 ÷ 41.67) × (√168.88 + √80.78) - 10% of 1499.85 = ?
√440.98 + (17.95% of 249.96 – 12% of 99.99) + (7.12)2 = ?
Which of the given trigonometric identities is incorrect ?
1. tan2 θ = sec2 θ - 1B. cosec2 θ = 1 + cot
What approximate value will come in place of the question mark (?) in the following question? (Note: You are not expected to calculate the exact value.)...
40.93√? + √6625 + √6920 + √? = 205.7542`xx` 7.654
What approximate value will come in place of the question mark (?) in the following question? (Note: You are not expected to calculate the exact value.)...
At a village trade fair a man buys a horse and a camel together for Rs 51,250. He sold the horse at a profit of 25 % and the camel at a loss of 20 %. If...
