Question

sec^4A+tan^4A=4/3 then tanA.secA​

Answer 1

tan A. sec A sec^4A.tan^4A

Answer 2

SOLUTION

GIVEN

$\displaystyle \sf{ { \sec}^{4} \theta + { \tan}^{4} \theta = \frac{4}{3} }$

TO DETERMINE

$\displaystyle \sf{ { \sec}^{} \theta \times { \tan}^{} \theta }$

EVALUATION

$\displaystyle \sf{ { \sec}^{4} \theta + { \tan}^{4} \theta = \frac{4}{3} }$

$\displaystyle \sf{ \implies \: {({ \sec}^{2} \theta - { \tan}^{2} \theta )}^{2} + 2 \times { \sec}^{2} \theta \times { \tan}^{2} \theta= \frac{4}{3} }$

$\displaystyle \sf{ \implies \: {(1)}^{2} + 2 { \sec}^{2} \theta { \tan}^{2} \theta= \frac{4}{3} }$

$\displaystyle \sf{ \implies \: 1 + 2 { \sec}^{2} \theta { \tan}^{2} \theta= \frac{4}{3} }$

$\displaystyle \sf{ \implies \: 2 { \sec}^{2} \theta { \tan}^{2} \theta= \frac{4}{3} - 1 }$

$\displaystyle \sf{ \implies \: 2 { \sec}^{2} \theta { \tan}^{2} \theta= \frac{1}{3} }$

$\displaystyle \sf{ \implies \: { \sec}^{2} \theta { \tan}^{2} \theta= \frac{1}{6} }$

$\displaystyle \sf{ \implies \: { \sec}^{} \theta { \tan}^{} \theta= \frac{1}{ \sqrt{6} } }$

FINAL ANSWER

$\displaystyle \sf{ \: { \sec}^{} \theta { \tan}^{} \theta= \frac{1}{ \sqrt{6} } }$

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