Math, asked by avulahema173, 5 hours ago

sec power 4 theta plus tan power 4 theta is equals to 4/3 then tan theta × sec theta is​

Answers

Answered by arunapatil140674
1

Answer:

1 sec 1000 time just 1 sec

Answered by pulakmath007
0

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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