Question
Download Solution PDFIf tan A + cot A = 2, then the value of 2(tan2 A + cot2 A) is :
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
tan A + cot A = 2
Calculation:
According to the question,
we have tan A + cot A = 2
Squaring both sides, we get
⇒ (tan A + cot A)2 = (2)2
⇒ tan2 A + cot2 A + 2(tan A)(cot A) = 4
⇒ tan2 A + cot2 A + 2(tan A)(1/tan A) = 4
⇒ tan2 A + cot2 A + 2 = 4
⇒ tan2 A + cot2 A = 2
Now,
2(tan2 A + cot2 A) = 2 × 2
⇒ 4
∴ The value of 2(tan2 A + cot2 A) is 4.
Shortcut Trick We can go with the value-putting method,
If we put A = 45° it satisfies the equation tan A + cot A = 2, so
2(tan2 A + cot2 A)
⇒ 2(1 + 1)
⇒ 4
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