Maharashtra State BoardHSC Science (General) 11th
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Select the correct option from the given alternatives: tanA1+secA+1+secAtanA is equal to - Mathematics and Statistics

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MCQ

Select the correct option from the given alternatives: 

`tan"A"/(1 + sec"A") + (1 + sec"A")/tan"A"` is equal to

Options

  • 2cosecA

  • 2secA

  • 2sinA

  • 2cosA

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Solution

2cosec A

Explanation:

`tan"A"/(1 + sec"A") + (1 + sec"A")/tan"A"`

= `(tan^2"A"+1+sec^2"A"+2sec"A")/((1+sec"A")tan"A")`

= `(sec^2"A"+sec^2"A"+2sec"A")/((1+sec"A")tan"A")` ......[∵ 1 + tan2A = sec2A]

= `(2sec"A"(sec"A"+1))/((1+sec"A")tan"A")=(2sec"A")/(tan"A")`

= `2/(sin"A")` = 2cosecA

Concept: Fundamental Identities
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APPEARS IN

Balbharati Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 2 Trigonometry - 1
Miscellaneous Exercise 2 | Q I. (2) | Page 32
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