Balaji Class 10 Maths Solutions Chapter 10 Trigonometrical Ratios and Identities Ex 10.3

Free PDF download of UP Board Solutions for Balaji Class 10 Maths Solutions Chapter 10 Trigonometrical Ratios and Identities Ex 10.3, are provided here, contain detailed explanations of all the problems mentioned in the UP Board Solutions. Students should solve questions from these UP Board solution of class 10, which will help them to prepare well for their exams.

Balaji Class 10 Maths Solutions Chapter 10 Trigonometrical Ratios and Identities Ex 10.3 त्रिकोणमितीय अनुपात एवं असमिकाएँ

Ex 10.3 Trigonometrical Ratios and Identities अतिलघु उत्तरीय प्रश्न (Very Short Answer Type Questions)

निम्न के मान ज्ञात कीजिए
प्रश्न 1.
sin(90° – θ)
हल:
sin(90° – θ) = cosθ

प्रश्न 2.
tan(90° + θ)
हल:
tan(90° + θ) = – cotθ

प्रश्न 3.
cos(180° – θ)
हलः
cos(180° – θ) (UPBoardSolutions.com) = – cosθ

प्रश्न 4.
cos37° cosec53°
हल:
cos37° cosec53° = cos 37°.cosec(90° – 37°) = cos 37° sec37° = cos 37°. $\frac{1}{\cos 37^{\circ}}$ = 1

प्रश्न 5.
tan210°
हलः
tan210° = tan(180° + 30°) = tan30° = $\frac{1}{\sqrt{3}}$

प्रश्न 6.
$\frac{\cos 55^{\circ}}{\sin 35^{\circ}}$
हलः

प्रश्न 7.
sin 225°
हलः
sin 225° = sin(180° + 45°) (UPBoardSolutions.com) = – sin 45° = $\frac{1}{\sqrt{2}}$

Ex 10.3 Trigonometrical Ratios and Identities लघु उत्तरीय प्रश्न-I (Short Answer Type Questions-I)

प्रश्न 8.
sin 27° sec63° का मान ज्ञात कीजिए|
हलः
sin 27°.sec 63° = sin 27°.sec(90° – 27°)
= sin 27°.cosec27°
=sin 27°. $\frac{1}{\sin 27^{\circ}}$ = 1

प्रश्न 9.
tan 37° tan 53° का मान ज्ञात कीजिए|
हलः
tan 37°.tan 53°= tan 37°. (UPBoardSolutions.com) tan(90° – 37°)
= tan37°.cot 37°
= tan37°. $\frac{1}{\tan 37^{\circ}}$ = 1

प्रश्न 10.
सिद्ध कीजिए: sin (180° + θ) = cos(90° + θ)
हलः
LHS → sin(180° + θ) = – sinθ
RHS → cos (90° + θ) = – sinθ
RHS = LHS

प्रश्न 11.
सिद्ध कीजिए: tan 45° – cot 45° = 0
हलः
LHS = tan 45° – cot (UPBoardSolutions.com) 45° = 1 – 1 = 0 = RHS

प्रश्न 12.
सिद्ध कीजिए: $\frac{\cos 21^{\circ}}{\sin 69^{\circ}}+\frac{\sin 59^{\circ}}{\cos 31^{\circ}}$ = 2
हलः

Ex 10.3 Trigonometrical Ratios and Identities लघु उत्तरीय प्रश्न-II (Short Answer Type Questions-II)

सिद्ध कीजिए कि
प्रश्न 13.
(i) sin 210°= – 1/2
(ii) tan 225°= 1
(iii) sec 210° = $-\frac{2}{\sqrt{3}}$
(iv) cosec 225°= $- \sqrt{{2}}$
हलः
(i) LHS = sin 210°= sin(180° + 30°) = – sin 30° = $-\frac{1}{2}$ = RHS
(ii) LHS = tan 225° = tan(180° + 45°) = tan 45° = 1 = RHS
(iii) LHS = sec 210° = sec(180° + 30°) (UPBoardSolutions.com) = – sec 30°= $-\frac{2}{\sqrt{3}}$ = RHS
(iv) LHS = cosec 225° = cosec(180° + 45° ) = – sec 45° = $- \sqrt{{2}}$ = RHS