If secθ−tanθ=45andsecθ+tanθ=m, then the value of (m+1)2 is equal to
A
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B
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C
5
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D
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Solution
The correct option is A Given : secθ−tanθ=45...(i)and,secθ+tanθ=m...(ii)Multiplying (i) and (ii), we get(secθ−tanθ)×(secθ+tanθ)=45×m⇒sec2θ−tan2θ=4m5⇒1=4m5(∵1+tan2θ=sec2θ)⇒m=54∴(m+1)2=(54+1)2=(94)2=8116
Hence, the correct answer is option a.