Prove that: sin 60 ° cos 30 ° + cos 60 ° · sin 30 ° = 1 .

Given that the trigonometrical expression is sin 60 ° cos 30 ° + cos 60 ° · sin 30 ° = 1 LHS = sin 60 ° cos 30 ° + cos 60 ° · sin 30 ° We know that, sin 60 ° = 3 2 , cos 30 ° = 3 2 , cos 60 ° = 1 2 and sin 30 ° = 1 2 = 3 2 3 2 + 1 2 1 2 = 3 4 + 1 4 = 1 = RHS Hence proved.

Prove that: cos 30 ° · cos 60 ° - sin 30 ° · sin 60 ° = 0 .

Given that the trigonometrical expression is cos 30 ° · cos 60 ° - sin 30 ° · sin 60 ° = 0 LHS = cos 30 ° · cos 60 ° - sin 30 ° · sin 60 ° We know that, sin 60 ° = 3 2 , cos 30 ° = 3 2 , cos 60 ° = 1 2 and sin 30 ° = 1 2 = 3 2 1 2 - 1 2 3 2 = 0 = RHS Hence proved.

Prove that: tan 60 ° + 1 tan 60 ° - 1 2 = 1 + cos 30 ° 1 - cos 30 ° .

Given that the trigonometrical expression is LHS = tan 60 ° + 1 tan 60 ° - 1 2 We know that, tan 60 ° = 3 ⇒ LHS = 3 + 1 3 - 1 2 = 4 + 2 3 4 - 2 3 = 1 + 3 2 1 - 3 2 = 1 + cos 30 ° 1 - cos 30 ° = RHS Hence proved.

Prove that: cos 2 × 30 ° = 1 - tan 2 30 ° 1 + tan 2 30 ° .

Given that the trigonometrical expression is cos 2 × 30 ° = 1 - tan 2 30 ° 1 + tan 2 30 ° We know that, tan 30 ° = 1 3 R H S = 1 - tan 2 30 ° 1 + tan 2 30 ° ⇒ R H S = 1 - 1 3 1 + 1 3 = 1 2 L H S = cos 2 × 30 ° = cos 60 ° = 1 2 L H S = R H S .

Prove that: tan 2 × 30 ° = 2 tan 30 ° 1 - tan 2 30 ° .

Given that the trigonometrical expression is tan 2 × 30 ° = 2 tan 30 ° 1 - tan 2 30 ° We know that, tan 30 ° = 1 3 R H S = 2 tan 30 ° 1 - tan 2 30 ° = 2 1 3 1 - 1 3 = 3 L H S = tan 2 × 30 ° = tan 60 ° = 3 L H S = R H S .

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Concise Mathematics I.C.S.E - Class IX>Trigonometry>Chapter 23 - Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]>EXERCISE

R K Bansal Solutions for Exercise 1: EXERCISE

Author:R K Bansal

R K Bansal Mathematics Solutions for Exercise - R K Bansal Solutions for Exercise 1: EXERCISE

Attempt the practice questions from Exercise 1: EXERCISE with hints and solutions to strengthen your understanding. Concise Mathematics I.C.S.E - Class IX solutions are prepared by Experienced Embibe Experts.