How do you find the value of #cos105# without using a calculator? Trigonometry Right Triangles Trigonometric Functions of Any Angle 1 Answer Anish M. Mar 26, 2018 #cos105# = #(1-sqrt3)/(2sqrt2)# Explanation: You can write #cos(105)# as #cos(45+60)# Now, #cos(A+B)=cosAcosB-sinAsinB# So, #cos(105)=cos45cos60-sin45sin60# =#(1/sqrt2)*(1/2)-(1/sqrt2)((sqrt3)/2)# =#(1-sqrt3)/(2sqrt2)# Answer link Related questions How do you find the trigonometric functions of any angle? What is the reference angle? How do you use the ordered pairs on a unit circle to evaluate a trigonometric function of any angle? What is the reference angle for #140^\circ#? How do you find the value of #cot 300^@#? What is the value of #sin -45^@#? How do you find the trigonometric functions of values that are greater than #360^@#? How do you use the reference angles to find #sin210cos330-tan 135#? How do you know if #sin 30 = sin 150#? How do you show that #(costheta)(sectheta) = 1# if #theta=pi/4#? See all questions in Trigonometric Functions of Any Angle Impact of this question 23889 views around the world You can reuse this answer Creative Commons License