Write True' or False' and justify your answer in each of the following :(i) The value of sin θ is x + 1x, where 'x' is a positive real number .(ii) cos θ = a2 + b22ab, where a and b are two distinct numbers such that ab > 0.(iii) The value of cos223 - sin267 is positive .(iv) The value of the expression sin 80° - cos 80° is negative .(v) The value of sin θ + cos θ is always greater than 1 .

Write True' or False' and justify your answer in each of the following

1.	Write True' or False' and justify your answer in each of the following :(i) The value of sin θ is x + 1x, where 'x' is a positive real number .(ii) cos θ = a2 + b22ab, where a and b are two distinct numbers such that ab > 0.(iii) The value of cos223 - sin267 is positive .(iv) The value of the expression sin 80° - cos 80° is negative .(v) The value of sin θ + cos θ is always greater than 1 .
Answer» Write True' or False' and justify your answer in each of the following : (i) The value of $\sin θ$ is $x + \frac{1}{x}$ , where 'x' is a positive real number . (ii) $\cos θ = \frac{a^{2} + b^{2}}{2 ab}$ , where a and b are two distinct numbers such that ab > 0. (iii) The value of $\cos^{2} 23 - \sin^{2} 67$ is positive . (iv) The value of the expression $\sin 80^{°} - \cos 80^{°}$ is negative . (v) The value of $\sin θ + \cos θ$ is always greater than 1 .