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If \( sin\theta =\frac{3}{5},\) then the value of \( (tan\theta +sec\theta {)}^{2} \)is
(A) 2
(B) 4
(C) 6
(D) 8

Answer

(B)
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Solution

Here, \( sin\theta =\frac{3}{5}\)
\( A{B}^{2}=25-9\)
\( AB=4\)
\( \therefore\;tan\theta =\frac{3}{4},  sec\theta =\frac{5}{4} \)
\( \therefore (tan\theta +sec\theta {)}^{2}\)
\( ={\left(\frac{3}{4}+\frac{5}{4}\right)}^{2}={\left(\frac{8}{4}\right)}^{2}=(2{)}^{2}=4\)
Solution for If  sintheta =frac{3}{5}, then the value of  (tantheta +sectheta {)}^{2} is(A) 2(B) 4(C) 6 (D) 8
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