Prove that Cot A -1 - 2- 2 A- A 1-tan A

cot A 1 / 2 sec2A = cot A 1 / 2 (1+tan2A) = cot A 1 / 1 tan2A = (1/tanA ) 1 / 1 tan2A [cotA =1/tanA] =(1 tanA) /tanA / 1 tan2A [Taking LCM] = (1 tanA) / ...

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Standard X

Mathematics

Standard Values of Trigonometric Ratios

Prove that Co...

Question

Prove that Cot A -1 / 2- sec^{2 A = cot A/ 1+tan A}

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Solution

cot A-1 / 2-sec²A

= cot A-1 / 2-(1+tan²A)

= cot A-1 / 1-tan²A

= (1/tanA ) -1 / 1-tan²A [cotA =1/tanA]

=(1-tanA) /tanA / 1-tan²A [Taking LCM]

= (1-tanA) /tanA / (1+tanA)(1-tanA) [a²-b² = (a+b)(a-b)]

=(1/tanA) / 1+tanA

= cotA / 1+tanA [1/tanA= cotA]

Proved

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Prove that Cot A -1 / 2- sec​2 A = cot A/ 1+tan A

cot A-1 / 2-sec2A = cot A-1 / 2-(1+tan2A) = cot A-1 / 1-tan2A = (1/tanA ) -1 / 1-tan2A [cotA =1/tanA] =(1-tanA) /tanA / 1-tan2A [Taking LCM] = (1-tanA) /tanA / (1+tanA)(1-tanA) [a2-b2 = (a+b)(a-b)] =(1/tanA) / 1+tanA = cotA / 1+tanA [1/tanA= cotA] Proved

Prove that Cot A -1 / 2- sec^{2 A = cot A/ 1+tan A}

cot A-1 / 2-sec²A

= cot A-1 / 2-(1+tan²A)

= cot A-1 / 1-tan²A

= (1/tanA ) -1 / 1-tan²A [cotA =1/tanA]

=(1-tanA) /tanA / 1-tan²A [Taking LCM]

= (1-tanA) /tanA / (1+tanA)(1-tanA) [a²-b² = (a+b)(a-b)]

=(1/tanA) / 1+tanA

= cotA / 1+tanA [1/tanA= cotA]

Proved