Question

1 + tan2A is equal to ……..​

Answer 1

Answer:

1+tan²(a) = sec²(a)

Step-by-step explanation:

1+tan²(a)

= sec²(a)

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Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

1 + tan²A =

(a) sin²A

(b) cos²A

(c) sec²A

(d) cosec²A

EVALUATION

$\displaystyle \sf{1 + { \tan}^{2}A }$

$\displaystyle \sf{ = 1 + \frac{ { \sin}^{2}A}{ { \cos}^{2}A} }$

$\displaystyle \sf{ = \frac{ { \cos}^{2}A + { \sin}^{2}A}{ { \cos}^{2}A} }$

$\displaystyle \sf{ = \frac{{ \sin}^{2}A + { \cos}^{2}A }{ { \cos}^{2}A} }$

$\displaystyle \sf{ = \frac{1}{ { \cos}^{2}A} }$

$\displaystyle \sf{ ={ \sec}^{2}A}$

FINAL ANSWER

Hence the correct option is (c) sec²A

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