Solve:(sec 35 degrees) (csc 55 degrees) - (tan 35 degrees) (cot 55 degrees)
I will skip the ° signs, so let's assume our numbers are degrees
also recall that because of complementary angles
sinA = cos(90-A)
tanA = cot(9-A)
so ...
(sec 35) (csc 55) - (tan 35) (cot55)
= 1/((cos35)(sin55)) - ((sin35)/cos35)) (cos55/sin55)
= 1/((sin55)(sin55)) - (cos55/sin55 ) (cos55/sin55)
= (1 - cos^2 55)/ sin^2 55
= sin^2 55/sin^2 55
= 1
Oh, ok thanks. I understand it now.
you are welcome
To solve the expression (sec 35 degrees)(csc 55 degrees) - (tan 35 degrees)(cot 55 degrees), we need to evaluate the trigonometric functions at the given angles and perform the necessary calculations.
1. Start by evaluating the trigonometric functions at the given angles.
sec 35 degrees = 1/cos 35 degrees
csc 55 degrees = 1/sin 55 degrees
tan 35 degrees = sin 35 degrees / cos 35 degrees
cot 55 degrees = cos 55 degrees / sin 55 degrees
2. Substitute the values into the expression.
(1/cos 35 degrees)(1/sin 55 degrees) - (sin 35 degrees / cos 35 degrees)(cos 55 degrees / sin 55 degrees)
3. Simplify by multiplying the numerators and denominators.
(1 * 1) / (cos 35 degrees * sin 55 degrees) - (sin 35 degrees * cos 55 degrees) / (cos 35 degrees * sin 55 degrees)
4. Combine the fractions.
(1 - sin 35 degrees * cos 55 degrees) / (cos 35 degrees * sin 55 degrees)
5. Use trigonometric identities to simplify further.
sin (A + B) = sin A * cos B + cos A * sin B
sin (35 degrees + 55 degrees) = sin 90 degrees = 1
Substitute the value into the expression.
(1 - sin 35 degrees * cos 55 degrees) / (cos 35 degrees * sin 55 degrees)
= (1 - 1 * cos 55 degrees) / (cos 35 degrees * sin 55 degrees)
= (1 - cos 55 degrees) / (cos 35 degrees * sin 55 degrees)
Now, the expression cannot be simplified further without knowing the values of cos 55 degrees, cos 35 degrees, and sin 55 degrees. You can use a calculator or reference table to find the specific values and substitute them into the expression to obtain the final result.