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Harlamova29_29 [7]
3 years ago
15

Write an expression that can be used to multiply 6 times 198 mentally

Mathematics
1 answer:
puteri [66]3 years ago
5 0
6*100
6*90
6*8

add them all up and you get 1188..the answer
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Verify cot x sec^4x=cotx +2tanx +tan^3x
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Answer:

See explanation

Step-by-step explanation:

We want to verify that:

\cot(x)  \:  { \sec}^{4} x =  \cot(x) + 2 \tan(x)   +  { \tan}^{3} x

Verifying from left, we have

\cot(x)  \:  { \sec}^{4} x  = \cot(x)  \: ( 1 +  { \tan}^{2} x )^{2}

Expand the perfect square in the right:

\cot(x)  \:  { \sec}^{4} x  = \cot(x)  \: ( 1 +  { 2\tan}^{2} x  + { \tan}^{4} x)

We expand to get:

\cot(x)  \:  { \sec}^{4} x  = \cot(x)  \:   +  \cot(x){ 2\tan}^{2} x  +\cot(x) { \tan}^{4} x

We simplify to get:

\cot(x)  \:  { \sec}^{4} x  = \cot(x)  \:   +  2 \frac{ \cos(x) }{\sin(x) ) }  \times  \frac{{ \sin}^{2} x}{{ \cos}^{2} x}   +\frac{ \cos(x) }{\sin(x) ) }  \times  \frac{{ \sin}^{4} x}{{ \cos}^{4} x}

Cancel common factors:

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This finally gives:

\cot(x)  \:  { \sec}^{4} x =  \cot(x) + 2 \tan(x)   +  { \tan}^{3} x

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