If 3 - - 4- x - then v2 x -1 - sin - 2 x is equal to

1/sin^2 x=cosec^2x,So above can be written as √cosec2α+2cotα=√1+cot2α+2cotα=|1+cotα| But 3π4 lt;α lt;π⇒cotα lt;−1⇒1+cotα lt;0 Hence, |1+cotα|=−(1+cotα ...

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Standard X

Mathematics

Standard Values of Trigonometric Ratios

If 3 π / 4< x...

Question

If 3π/4 < x < π, then √(2cot x + 1/sin^2 x) is equal to____

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Solution

1/sin^2 x=cosec^2x,So above can be written as
√cosec2α+2cotα=√1+cot2α+2cotα=|1+cotα|
But 3π4<α<π⇒cotα<−1⇒1+cotα<0
Hence, |1+cotα|=−(1+cotα)

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If 3π/4 < x < π, then √(2cot x + 1/sin^2 x) is equal to____

1/sin^2 x=cosec^2x,So above can be written as √cosec2α+2cotα=√1+cot2α+2cotα=|1+cotα| But 3π4<α<π⇒cotα<−1⇒1+cotα<0 Hence, |1+cotα|=−(1+cotα) We found a similar question to the one that you posted. Please check it out here.

1/sin^2 x=cosec^2x,So above can be written as
√cosec2α+2cotα=√1+cot2α+2cotα=|1+cotα|
But 3π4<α<π⇒cotα<−1⇒1+cotα<0
Hence, |1+cotα|=−(1+cotα)

We found a similar question to the one that you posted. Please check it out here.