The document Short Answer Type Questions(Part- 1)- Introduction to Trigonometry Class 10 Notes | EduRev is a part of the Class 10 Course Mathematics (Maths) Class 10.

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**Q1. It is given that tan (Î¸ _{1} + Î¸_{2}) = where Î¸_{1} and Î¸_{2} areacute angles. Calculate Î¸_{1} + Î¸_{2} when tan Î¸_{1}**

Now,tan (Î¸_{1} + Î¸_{2}) = 1 â‡’ Î¸_{1} + Î¸_{2} = 45Â°.

**Q2. Prove that: **

**Q3. Prove that: (sin ^{4} Î¸ â€“ cos^{4} Î¸ +1) cosec^{2} Î¸ = 2 **

**Sol. **L.H.S.

= (sin^{4} Î¸ â€“ cos^{4} Î¸ + 1) cosec^{2} Î¸

= [(sin^{2} Î¸)^{2} â€“ (cos^{2} Î¸)^{2} + (sin^{2} Î¸ + cos^{2}Î¸)] cosec^{2} Î¸ [âˆµ sin^{2} Î¸ + cos^{2} Î¸ = 1]

= [(sin^{2} Î¸ â€“ cos^{2} Î¸) (sin^{2} Î¸ + cos^{2} Î¸) + (sin^{2}Î¸ + cos^{2} Î¸)] cosec^{2} Î¸

= [(sin^{2} Î¸ â€“ cos^{2} Î¸) 1 + 1] cosec^{2} Î¸

= (sin^{2} Î¸ â€“ cos^{2} Î¸) + cosec^{2} Î¸

= [(sin^{2} Î¸ + (1 â€“cos^{2} Î¸)] cosec^{2} Î¸

= [sin^{2} Î¸ + sin^{2} Î¸] cosec^{2} Î¸ [âˆµ 1 â€“ cos^{2} Î¸ = sin^{2} Î¸]

= 2 sin2 Î¸ . cosec^{2} Î¸

= 2 = RHS [âˆµ sin Î¸ . cosec Î¸ = 1]

**Q4. Prove that: sec ^{2} Î¸ + cosec^{2} Î¸ = sec^{2} Î¸ Â· cosec^{2} Î¸ **

**Sol. **L.H.S. = sec^{2} Î¸ + cosec^{2} Î¸

**Q6. Given that Î± + Î² = 90Â°, show that: **

**Sol.** âˆµ Î± + Î² =90Â°

âˆµ Î² = (90 â€“ a)

**Q10. Prove that: sin ^{6}Î¸ + cos^{6}Î¸ + 3sin^{2}Î¸ cos^{2}Î¸ = 1.**

**Sol. **âˆµ sin2 **Î¸** + cos2**Î¸** = 1

âˆµ (sin^{2} **Î¸** + cos^{2} **Î¸**)3 = (1)3 = 1

â‡’ (sin^{2} Î¸) 3 + (cos^{2} Î¸)^{3} + 3 sin^{2} Î¸ . cos^{2} Î¸ (sin^{2} Î¸ + cos^{2} Î¸) = 1

â‡’ sin^{6} Î¸ + cos^{6} Î¸ + 3 sin^{2} Î¸ . cos^{2}Î¸ (1) = 1

â‡’ sin^{6} Î¸ + cos^{6} Î¸ + 3 sin^{2} Î¸ . cos^{2} Î¸ = 1

**Q11. Prove that: a ^{2} + b^{2} = x^{2} + y^{2} when a cos Î¸ âˆ’ b sin Î¸ = x and a sin Î¸ + b cos Î¸ = y.**

= 2 cosec A

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