Question

tan2 135-sec2 60=xsin135*cos45*tan60

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

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5E

1.a.Soln: LHS = sec θ . cosec (90° ‒ θ) ‒ tan θ . cot (90° ‒ θ)

= sec θ . sec θ – tan θ . tan θ = sec2θ–tan2θ = 1 = RHS proved

b. Soln: LHS = tan2A .sec2(90–A)–sin2A cosec2 (90–A)

= tan2A cosec2A–sin2A sec2A

= sin2Acos2A.1sin2A−sin2A.1cos2A=1cos2A−sin2Acos2A=1−sin2Acos2A=cos2Acos2A=1=RHSproved

c. Soln: LHS = sinθsec(π2−θ)−cosecθcos(π2−θ)

= sinθ cosecθ–cosecθ sinθ = 1 – 1 = 0 = RHS proved

d. Soln: LHS = sin2(π2−θ)cosecθ−tan2(π2−θ)sinθ

= cos2θ cosecθ–cot2θ sinθ = cos2θsin2θ−cos2θsin2θ.sinθ

= cos2θsinθ−cos2θsinθ=cos2θ−cos2θsinθ = 0 = RHS proved

e. Soln: LHS = cotθ + cot(π2−θ) = cotθ + tanθ = cosθsinθ+sinθcosθ=cos2θ+sin2θsinθ.cosθ=1sinθ.cosθ=1sinθ.1cosθ

= cosecθ secθ = cosecθ .cosec(π2−θ)=RHSproved

f. Soln :LHS =

= cos2θcos2θ = 1 = RHS proved

2. a. Soln: LHS = sin420°.cos390° + cos( –300°).sin( –330°)

= sin420° . cos390° + cos300°.sin( –330°)

= sin420°.cos390°–cos300°.sin(330°)

= sin(360° + 60°).cos(360° + 60°)–cos(360°–60°).sin(360°–30°)

= sin60° cos30°–cos60°( –sin30°)

= 3√2∗3√2+12∗12=34+14=44=1=RHSproved

b. Soln: LHS = cos120°.sin150° + cos330°.sin300°

= cos120°.sin150° + cos(360°–30°).sin(360°–60°)

= cos120°.sin150° + cos30°.sin( –60°)

= cos120°.sin150°–cos30°.sin60°

= −12∗12−3√2∗3√2=−34−14=−44=−1=RHSproved

c. Soln: LHS = cos240°.sin300° – sin330°.cos300°

= cos(180° + 60°) sin(360° – 60°) – sin(360° – 30°) cos(360° – 60°)

= –cos60°( –sin60°) –( –sin30°)cos60°

= cos60° sin60° + sin30°cos60°

=12∗3√2+12∗12=3√4+14=1+3√4=RHSproved

d. Soln: LHS = cos240°.cos120° – sin120°.cos150°

= cos(180° + 60°)cos120° – sin120°.cos150°

= –cos60°cos120° – sin120°cos150°

=−12∗(−1)2−3√2∗(−3√)2=34+14=44=1=RHSproved

3. a. Soln: LHS = sin65° + cos35°

= sin(90° – 25°) + cos(90° – 55°)

= cos25° + sin55° = RHS proved

b. Soln: LHS = tan9°.tan27°

= tan(90° – 81°).tan(90° – 63°)

= cot63°.cot81° = RHS proved

c. Soln: LHS = cos25°.cos65° – sin25°.sin65°

= cos25°.cos65° – sin(90° – 65°).sin(90° – 25°)

= cos25°.cos65 – cos25°.cos65 = 0 = RHS proved

d. Soln: LHS = tan32° + cot53° – cosec80°

= tan(90° – 58°) + cot(90° – 37°) – cosec(90° – 10°)

= cot58° + tan37° – sec10° = RHS proved

e. Soln: LHS = sin81° + sec54° + tan18°

= sin(90° – 9°) + sec(90° – 36°) – tan(90° – 72°)

= cos9° + cosec36° + cot72° = RHS proved

f. Soln: LHS = sin9°.sin27°.sin63°.sin81°

= sin(90° – 81°).sin(90° – 63°).sin(90° – 27°).sin(90° – 9°)

= cos81°.cos63°.cos27°.cos9° = RHS proved

g. Soln: LHS = tan9°.tan27°.tan45°.tan63°.tan81°

= tan(90° – 81°).tan(90° – 63°).tan45°.tan63°.tan81°

= cot81°.cot63°.tan45°.tan63°.tan81°

(cot81°tan81°)(cot63°tan63°)tan45° = 1 × 1 × 1 = 1 = RHS proved