Trigonometrical Equations 1 Question 23

23. General value of θ satisfying the equation tan2θ+sec2θ=1 is……. (1996, 1M)

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Answer:

Correct Answer: 23. θ=mπ,nπ±π3

Solution:

  1. Given, tan2θ+sec2θ=1

tan2θ+1cos2θ=1tan2θ+1+tan2θ1tan2θ=1tan2θ(1tan2θ)+(1+tan2θ)=1tan2θ3tan2θtan4θ=0tan2θ(3tan2θ)=0tanθ=0 or tanθ=±3

Now, tanθ=0θ=mπ, where m is an integer.

 and tanθ=±3=tan±π3θ=nπ±π3

θ=mπ,nπ±π3, where m and n are integers.



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