CBSE Guess > Papers > Important Questions > Class X > Maths > Mathematics By Mr. Sanjay Kumar Chapter - 12
Q. 126. Prove that: (i) tan2θ – sin2θ = tan2θ sin2θ = sin4θ sec2θ. (ii) tan2θ + cot2θ + 2 = sec2θ cosec2θ. Q. 127. Prove that: (i) tan4A + tan2A = sec4A – sec2A. (ii) (cosec θ – cot θ)2 = (1– cos θ) / (1+cos θ). Q. 128. If sec θ + cos θ = 2, then find the values of: (i) sec3 θ + cos3 θ = ? (ii) ( sec2 θ + cos2 θ )2 = ? (iii) sec7 θ + cos7 θ = ? Q. 129. Prove that ( tan A + cosec B )2 – ( cot B – sec A )2 = 2 tan A cot B ( cosec A + sec B ). Q. 130. Prove: (i) (sinθ + cosecθ)2 + (cos θ + sec θ)2 = 7 + tan2 θ + cot2 θ. (ii) (sinθ + secθ)2 + (cosθ + cosecθ)2 = (1 + secθ cosecθ)2. Q. 131. Prove that: 2 sec2 θ – sec4 θ – 2 cosec² θ + cosec4 θ = cot4 θ – tan4 θ. Q. 132. Evaluate: ( 3 sin2 46˚– 5sec2 35˚ + 3 sin2 44˚ + 5 cot2 55˚) + ( cos 1˚ cos 2˚ cos 3˚ …………….cos 100˚). Q. 133. Prove that: (i) tan θ / (1 – cot θ) + cot θ / (1 – tan θ) = 1 + tan θ + cot θ. (ii) sin6 θ + cos6 θ = 1 – 3 sin2 θ cos2 θ. Q. 134. Prove that: (i) tan A (1 – cot2 A) + cot A (1 – tan² A) = 0. (ii) ( 1 + tan A tan B)2 + (tan A – tan B)2= sec2 A sec² B. Q. 135. Prove that: (i) (secθ+tanθ–1) / (tanθ–secθ+1) = cosθ / (1–sinθ). (ii) Prove that: cotθ (2–sec²θ) = (1+tanθ) (cotθ–1). Q. 136. Evaluate: (i) sin (55˚– θ) + sin( 50˚ + θ) – cos(35˚ + θ) – cos (40˚– θ) – cot2 θ + sec2 (90˚ – θ). Q. 137. Prove that: (i) tan 10˚ tan 75˚ tan 15˚ tan 80˚ = 1. (ii) sin2 (90˚ – θ) [1 + cot2 (90˚ – θ)] = 1. Q. 138. Evaluate: cot θ tan (90˚– θ) – sec (90˚ – θ) cosec θ + √3 ( tan 5˚ tan 30˚ tan 75˚ tan 85˚) + sin2 25˚ + sin2 65˚. Q. 139. Prove that: (i) sec4 A (1 – sin4 A) – 2 tan2 A = 1. (ii) If p = cosec θ – sin θ , q = sec θ – cos θ, prove: p2q2 (p2+q2+3) = 1. Q. 140. (i) If cos θ – sin θ = 1, then prove that cos θ + sin θ = ± 1. (ii) Solve for θ: 2 cos2 θ + sin θ – 2 = 0.
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