Question

If sec A = sqrt2
find
3 cot^2(A) + 2 sin^2(A)/tan^2(A) - cos^2(A)

Answer 1

@perl

Answer 2

@perl

Answer 3

@ganeshie8

Answer 4

@Compassionate

Answer 5

@Preetha
@Palmo4ka
@Somy
@Hero
@IrishBoy123

Answer 6

If we apply the definition of sec(A), then we can write:
\[\frac{1}{{\cos \left( A \right)}} = \sqrt 2 \]

Answer 7

cos(A) = 1/sqrt2

Answer 8

ok!

Answer 9

Now?

Answer 10

please you can compute (sin(A))^2, using the fundamental identity, namely:
\[{\left( {\sin \left( A \right)} \right)^2} = 1 - {\left( {\cos \left( A \right)} \right)^2} = ...?\]

Answer 11

1 - 1/2?

Answer 12

yes!

Answer 13

1/2?

Answer 14

yes!

Answer 15

now?

Answer 16

now please use these identities, in order to find:
(Tan(A))^2, and (cot(A))^2:
\[\begin{gathered}
{\left( {\tan \left( A \right)} \right)^2} = \frac{1}{{{{\left( {\cos \left( A \right)} \right)}^2}}} - 1 = 2 - 1 = ...? \hfill \\
{\left( {\cot \left( A \right)} \right)^2} = \frac{1}{{{{\left( {\sin \left( A \right)} \right)}^2}}} - 1 = 2 - 1 = ...? \hfill \\
\end{gathered} \]

Answer 17

1 and 1?

Answer 18

perfect!

Answer 19

finally, substitute those values, namely:
\[\begin{gathered}
{\left( {\sin \left( A \right)} \right)^2} = {\left( {\cos \left( A \right)} \right)^2} = \frac{1}{2} \hfill \\
{\left( {\tan \left( A \right)} \right)^2} = {\left( {\cot \left( A \right)} \right)^2} = 1 \hfill \\
\end{gathered} \]
into your original expression:
\[\frac{{3{{\left( {\cot \left( A \right)} \right)}^2} + 2{{\left( {\sin \left( A \right)} \right)}^2}}}{{{{\left( {\tan \left( A \right)} \right)}^2} - {{\left( {\cos \left( A \right)} \right)}^2}}} = ...?\]

Answer 20

sin was 1/2 right?

Answer 21

I mean sin(A) = 1/2?

Answer 22

no, please:
\[\sin \left( A \right) = \frac{1}{{\sqrt 2 }}\]

Answer 23

sorry forgot the ^2 sign
and please continue

Answer 24

ok! Please what is:
\[\frac{{3{{\left( {\cot \left( A \right)} \right)}^2} + 2{{\left( {\sin \left( A \right)} \right)}^2}}}{{{{\left( {\tan \left( A \right)} \right)}^2} - {{\left( {\cos \left( A \right)} \right)}^2}}} = \frac{{3 \cdot 1 + 2 \cdot \frac{1}{2}}}{{1 - \frac{1}{2}}} = ...?\]

Answer 25

3-1/1 - 1/2?

Answer 26

no, please:
\[\frac{{3{{\left( {\cot \left( A \right)} \right)}^2} + 2{{\left( {\sin \left( A \right)} \right)}^2}}}{{{{\left( {\tan \left( A \right)} \right)}^2} - {{\left( {\cos \left( A \right)} \right)}^2}}} = \frac{{3 \cdot 1 + 2 \cdot \frac{1}{2}}}{{1 - \frac{1}{2}}} = \frac{{3 + 1}}{{\frac{1}{2}}} = \frac{4}{{\frac{1}{2}}} = 4 \cdot 2 = ...?\]

Answer 27

8.

Answer 28

that's right!

Answer 29

can you help me with a few more problems?

Answer 30

yes! Please wait I have to go to lunch

Answer 31

I'll post a new question and tag you okay??