Solve = tan5 .cot20 1- cos10 cos40 cos50 ° 1 cos10 cos40 ° cos50 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$\frac { 1 - \cos 10 ^ { \circ } + \cos 40 ^ { \circ } - \cos 50 ^ { \circ } } { 1 + \cos 10 ^ { \circ } - \cos 40 ^ { \circ } - \cos 50 ^ { \circ } } = \tan 5 ^ { \circ } \cdot \cot 20 ^ { \circ }$$

Verify

$\text{false}$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{1 - 0.984807753012208 + 0.766044443118978 - 0.6427876096865394}{1 + 0.984807753012208 - 0.766044443118978 - 0.6427876096865394} = 0.2444651379156608$$

Subtract $0.984807753012208$ from $1$ to get $0.015192246987792$.

$$\frac{0.015192246987792+0.766044443118978-0.6427876096865394}{1+0.984807753012208-0.766044443118978-0.6427876096865394}=0.2444651379156608$$

Add $0.015192246987792$ and $0.766044443118978$ to get $0.78123669010677$.

$$\frac{0.78123669010677-0.6427876096865394}{1+0.984807753012208-0.766044443118978-0.6427876096865394}=0.2444651379156608$$

Subtract $0.6427876096865394$ from $0.78123669010677$ to get $0.1384490804202306$.

$$\frac{0.1384490804202306}{1+0.984807753012208-0.766044443118978-0.6427876096865394}=0.2444651379156608$$

Add $1$ and $0.984807753012208$ to get $1.984807753012208$.

$$\frac{0.1384490804202306}{1.984807753012208-0.766044443118978-0.6427876096865394}=0.2444651379156608$$

Subtract $0.766044443118978$ from $1.984807753012208$ to get $1.21876330989323$.

$$\frac{0.1384490804202306}{1.21876330989323-0.6427876096865394}=0.2444651379156608$$

Subtract $0.6427876096865394$ from $1.21876330989323$ to get $0.5759757002066906$.

$$\frac{0.1384490804202306}{0.5759757002066906}=0.2444651379156608$$

Expand $\frac{0.1384490804202306}{0.5759757002066906}$ by multiplying both numerator and the denominator by $10000000000000000$.

$$\frac{1384490804202306}{5759757002066906}=0.2444651379156608$$

Reduce the fraction $\frac{1384490804202306}{5759757002066906}$ to lowest terms by extracting and canceling out $2$.

$$\frac{692245402101153}{2879878501033453}=0.2444651379156608$$

Convert decimal number $0.2444651379156608$ to fraction $\frac{38197677799322}{10000000000}$. Reduce the fraction $\frac{38197677799322}{10000000000}$ to lowest terms by extracting and canceling out $2$.

$$\frac{692245402101153}{2879878501033453}=\frac{19098838899661}{78125000000000}$$

Least common multiple of $2879878501033453$ and $78125000000000$ is $224990507893238515625000000000$. Convert $\frac{692245402101153}{2879878501033453}$ and $\frac{19098838899661}{78125000000000}$ to fractions with denominator $224990507893238515625000000000$.

$$\frac{54081672039152578125000000000}{224990507893238515625000000000}=\frac{55002335541835123545871359433}{224990507893238515625000000000}$$

Compare $\frac{54081672039152578125000000000}{224990507893238515625000000000}$ and $\frac{55002335541835123545871359433}{224990507893238515625000000000}$.

$$\text{false}$$