176 If 0 theta2 theta1 pi/4, cos(theta1 + theta2) = 3/5 and cos( - Maths - Trigonometric Functions

Question

176 If 0 < theta2 < theta1 < pi/4,
cos(theta1 + theta2) = 3/5 and cos(
theta1 - theta2) = 4/5, then
sin2theta1 equal to
i) -1
ii) 1
iii) 2
iv) -2

Arpita D Pal · Accepted Answer

Dear Student, from the given θ1+θ2= cos-135and'θ1-θ2= cos-145add both 2θ1= cos-135+ cos-145= cos-135×45-1-3521-452=cos-1025=π22θ1=π2so sin2θ1=sin90 = 1formula  cos-1x+ cos-1y= cos-1xy-1-x21-y2Regards

176. If 0 < theta2 < theta1 < pi/4, cos(theta1 + theta2) = 3/5 and cos( theta1 - theta2) = 4/5, then sin2theta1 equal to i) -1 ii) 1 iii) 2 iv) -2

176. If 0 < theta₂ < theta₁ < pi/4, cos(theta₁ + theta₂) = 3/5 and cos( theta₁ - theta₂) = 4/5, then sin2theta₁ equal to
i) -1
ii) 1
iii) 2
iv) -2