Question

Evaluate :
cos(45+0) + cos² (45-0)
+(cot 30° + sin 90°) (tan 60° - sec 0°)
tan(60+0) x tan(30-0)​

Answer 1

Step by Step

Cos²(45°+x)+cos²(45°-x)

= Cos²(45°+x)+Sin²(90 - (45°-x))

= Cos²(45°+x)+Sin²(45°+x)

= 1

tan(60°+x)  + tan(30°-x)

= Cot (90 - (60 + x))   + tan(30°-x)

= Cot (30 - x) + tan(30°-x)

= Cos(30 -x)/Sin(30-x)  + Sin(30-x)/Cos(30-x)

= (Cos²(30 -x) + Sin²(30-x))/Sin(30-x) Cos(30-x)

= 1/Sin(30-x) Cos(30-x)

=> Cos^2(45°+x)+cos^2(45°-x)/tan(60°+x)+ tan(30°-x) = Sin(30-x) Cos(30-x)

(cot30°+sin 90°)×(tan60°-sec0°)

= (√3 + 1)(√3 - 1)

= 3 - 1

= 2

= Sin(30-x) Cos(30-x) + 2